As long as game balance has existed (probably), it has been believed that balance and variety are opposite of each other, as having more characters or whatnot makes it harder to find the overpowered stuff and balance out everything. However, saying this is practically forgetting the whole point of game balance in the first place: making sure people like Stop Having Fun Guys don't get away with picking the same characters again and again. Simply put, game imbalance virtually eliminates variety, because why use pet classes when the uber powerful Dragon Master Knight will just decimate them, quite possibly while avoiding banning territory? Now people like Hyperactive Girls most likely don't care what's the most powerful class or character or whatever, but no decent or even halfway decent person deserves a cheap defeat. (And by the way, you can argue that imbalance provides handicaps? I don't know, how about the game actually allow handicaps in a neon sign of some sort? It's unlikely the game needs to actively balance around that beyond avoiding things like Character Select Forcing.)
Of course, my argument isn't as simple as a reminder of the point of game balance. I have another thing to say: more variety means that the "balanced enough" area is bigger because of the higher number of threats to any character, so the requirements for solid balancing become less strict. When any character has only one threat to worry about (if that), they can just safeguard against that threat and be done with it. But against multiple threats, that's more effort required to throw them off. By no means is this a signal to get complacent, though. Game balance is still tricky business, so it's best to be diligent about it.
Now somebody requested that I answer whether I think characters should follow rock-paper-scissors or simply be different but without any advantages over each other. While the short answer is that I would find the latter ideal, I can use this post to talk about both because the balance/variety topic is related closely enough.
I'll talk about a rock-paper-scissors. This is used to provide deliberate imbalance in character matchups, which is sometimes a good thing, albeit not ideal. It's ideally used in army games, where there are so many units per side that the whole thing can get chaotic fast and finding actually broken stuff can easily become a chore because you can't judge easily what becomes too powerful without having bad matchups to keep them in check. There are two levels of countering: soft counters, where the matchup, while advantageous, can still be lost; and hard counters, where the matchup is a clear cut guaranteed victory. Hard counters particularly can be helpful if it means stopping units that can otherwise be readily abused, but be aware that if the numbers of decent units build up, suddenly Mighty Glaciers can become definite threats with nothing to either stop them from repeatedly hitting something, or kill them fast enough to stop considerable damage. Speed can only mean so much when the battlefield gets crowded, after all. Besides this, relying too much on hard counters is begging for creating a glorified version of simple rock-paper-scissors. But how do we even create the soft counters to begin with? Simple: provide each character/unit with traits. This allows them different behavior styles that can allow them to avoid suffering as much from losing a matchup.
There's a game that does a nice job with its ideas of balancing units with a rock-paper-scissors system: Battalion Wars. The only real problems is some execution flaws and variety issues, but here's the lowdown: even though rock-paper-scissors is in place, some matchups can be won despite disadvantage because each player controls an individual unit directly and commands their other units, per the mere concept of the game. AI units, having poor sense of survival (though it should be toned up a bit), can be continuously attacked and their numbers thinned to isolate the player's unit. This allows scenarios like Bazooka Vets obliterating or just plain lasting against Flame Vets due to being able to OHK them; vehicles including the Anti-Air Vehicle surviving Bazooka abuse while doing their job of grounding the air force; and even Fighters providing commands to hit distant ground targets they can't deal with themselves while throwing off any AA fire. The only real problems with the balance aside from map flaws such as underused units is lack of non-air speed units aside from the Recon (an underused unit to begin with, but also has a limited role), the underdeveloped navy, the excessive durability against MG fire that Recons and air units have, and just plain obvious flaws like (in BW2) the lack of distance penalties for Bazooka Vets humiliating emplacements, and the Battlestation's lack of Stone Wall status leading to excessively lopsided matchups. Of course, there are going to be SOME lopsided matchups, but a prime example of how they're not necessarily bad is the Flame Vets. They can't do anything to vehicles. Maybe do a little damage to Recons if they're lucky, but that's the best they can hope for. But as it turns out, infantry, the units they're effective against, cover at least 70% of the unit makeup. To stop them from becoming broken, Kuju limited their range so that they'd be Melee Tornadoes in a shooting game. Thus, outside of map flaws (Donatsu Island's slippery slope), they do not bend that 70% of the game to their will without effort, and the variety stays stable because they can be dealt with. In fact, it's improved with a reliable way to considerably reduce infantry numbers and punish them for attacking but gets countered by managing a thick defense.
So you might say that Tactical Rock Paper Scissors isn't bad, in fact more likely to make an army game more newbie friendly while avoiding being glorified by having subversions exist. But in games where dueling is the norm, you certainly don't want matches to have the winner determined by the character select screen. Rather, characters should have individual traits but not have blatant advantages over others, so that they have equal chance assuming good understanding of the individual characters. But how to do this?
Well, if there are only a few characters, one is more likely to stand out. Even if they don't flatly break the game, just being the best character is enough to make the game imbalanced. The problem is that the best character has fewer characters to worry about. Those few characters who manage to be a threat will get shortlisted, strategized around, and then the character can easily pick up the pieces as long as they don't get complacent. But with more characters, this becomes harder as more characters have working tools against the strong character(s)'(s) gimmick.
But naturally, this would actually prove stand-out characters more and more. If a low percentage of characters have the tools to deal with them, that would show how powerful those characters are. However, because it's harder to stand out, the characters that do can be hunted down just as easily. And it's not like game balance is an easy job. (Granted, it's also thankless in general, but if it wasn't necessary, this blog wouldn't exist.)
So what do we do to make sure of this? There are two things:
1) Check the mechanics
2) Check each character for potential excessive strength/weakness abuse
The first one, mechanics, would be checked to avoid having to give a character blatantly inflated stats just to make them a Skill Gate Character instead of a Joke Character. This actually happened with Ike, who has ridiculously high power and good melee range, but combine his low speed with his Melee Tornado status and you get a character who is easily hit if he tries any offense, then throw in SSB's unconditional flinching (aside from maybe TWO attacks TOTAL--out of about 22 per character and about 40 characters--and yes, 1/440 is such an awfully low ratio that any math errors on my part are irrelevant), excessive punishment for mistakes, and lack of effective equalizers when trailing by stock, and Ike suddenly looks like a terrible character. Yes, that's right, inflated power barely makes Ike even USEABLE.
This is a common pitfall: most of the time, the Game Breaker is guaranteed to be a Fragile Speedster, even if whoever it is isn't agreed on. Mighty Glaciers, meanwhile, have to get seemingly broken stats to be viable. This is likely a mechanics problem. It is therefore advised to watch how you handle the gameplay. Keep in mind that speedsters can be powerful easily by getting a high amount of zone quickly, so it's vital that the quantity of base zone control is *NOT* a critical factor. Of course, making Mighty Glaciers easily unkillable in any halfway reasonable time frame is not exactly inspiring either, but if mechanics provide them plenty of feasible options, they'd be able to do various things and thus keep up with the faster characters and devastate the weaker ones who don't access their other strengths. Anybody who has been relying on speed will simply get trapped and pounded. Slow and steady wins the race.
As for the second one, this one is actually in regards to matchups. Need an example? Let's go with something that most people should know:
In the red corner, weighing in at 146 pounds, the Bare Fisted Monk, a warrior who is so good at being a Melee Tornado that he can beat down pretty much ANYBODY as soon as he gets close up.
In the blue corner, weighing in at 128 pounds, the Squishy Wizard, a spellcaster who acts as a Frail Sniper by using spells to jackhammer his opponents unless he wants pretty much ANYBODY to get close up and beat him down as a result.
See where this is going? This matchup likes to have bothersome balance. If the SW has only distance attack spells to really defend themselves, either he rips apart the BFM by exploiting his inability to attack from a distance and likely low Magic Defense, or the BFM closes the distance and rips the SW apart. Here's what would be ideal: make sure the BFM can defend himself from distance attacks so that closing the distance isn't as urgent, and the SW has ways to deal with anybody who manages to close the distance on them so that they can survive their own mistakes.
Just be wary of potential aftereffects of reducing strengths or weaknesses too much, so that characters can stay unique, not to mention avoiding the possibility of somebody ending up broken. As long as you keep strengths and weaknesses at bearable levels, though, matchups can easily become less lopsided.
In closing, as they say, variety is the spice of life. It can also be the spice of balance.