Well first, champion design and balance should be one and the same, or at least such closely related teams that they're virtually indistinguishable. "Different teams" is not just a bad cop out. It's admitting that they don't really care about balance, if they have a team dedicated to putting out champions without balancing them...
What? I don't see why these need to be more involved than they already are. The balance team is definitely involved in champion releases, and the design team is involved in remakes and significant tweaks that affect a champion's feel.
If you're thinking of a way to make a champion unique and fun, I don't think you should need to care about balancing it until you've found a way to make it fun to play. It's probably not going to be released to the public for several months, the balance repurcussions don't exist quite yet.
And a designer doesn't need to know how to interpret data like win ratios and pick rates across various elos and modes to determine a champion's power. They don't need to test numbers changes for existing champions because that's a waste of time for them.
Balance should get involved at the end of design, and design should get involved when balance needs more than just numbers changes, and that's how things work currently. Saying otherwise is like saying that the concept artists should be the same people as the splash artists, but they're not for a reason. If you segregate your teams and only bring them together when they need to come together, you can get them to excel at more specific skills.
And regardless, the balance team will never ever be able to get things under control if the steady influx of new characters never slows down.
But keeping their own game in a state of being constantly broken is their business model. It's common knowledge among the player base.
The balance team has been pretty much constantly getting things under control for quite a while now. The game is way more balanced than it was a year ago. A far larger portion of champions are viable than were then, and everyone who says otherwise really has to be intentionally ignoring the evidence by now.
But keeping their own game in a state of being constantly broken is their business model. It's common knowledge among the player base.
I'm so tired of this conspiracy theory. They've put a lot of work into reworking Sivir mechanically (450 IP champion), put out an art rework out for Ashe (450 IP champion), they're currently working on an art rework for Soraka (450 IP champion), rework for Karma (3150 IP), huge rework for Eve (1350) and Twitch (3150).
Every time an OP champion comes out everyone's like OMG RIOT IS RELEASING OP CHAMPIONS TO MAKE MONEY and then every time they release a Sejuani, Yorick, or Hecarim everyone just shuts up until another OP one comes out so they can whine again.
And every time a 6300 is OP everyone whines about how Riot is trying to sell power, but when Sivir or Ashe are the best AD carry then everyone conveniently stops talking about price and power.
This is a huge example of the
Texas Sharpshooter fallacy. If you ignore all the overpowered low-priced champions, then yeah, it looks like they're selling power. But if you actually look at the data as a whole there's no correlation.
This I'm more forgiving of. I'm one of those who only plays summoner's rift. Although, that's mainly because I'm a defensive style player who prefers a slow, strategic march.
Still, there's no reason for them not to experiment more with the genre formula, which has thus far been explored very little. The only thing they openly experiment with is champion design, but there are soooooo many other variables and potential innovations that could be toyed with. It's not like the risks are at all the same as with champion releases. If people don't like a map or game mode, they simply won't play it. Little harm done. Compare to the risk of putting out a broken champion, which is intrusive to everyone's game experience.
Risks? The resources for creating a map and testing balance on it, making art for the whole thing, etc are huge and that would be largely wasted. Also going "hey, pump out a map without caring as much about it" is against everything that the community has asked for in every other part of the game.
At least as far as I've seen, everyone is pretty fine with slowing down champion production rates if it means better/more polished champions. And also everyone is ecstatic with skins like Draven's launch skin (huge model differences, modified voiceover, new particles, etc) rather than him being launched with two lower quality skins. Despite the community really wanting everything as soon as they can, when something actually comes out they're very dissatisfied with rushed results (see: 34% bonus IP weekend) and very happy with a well-done product.
And finally, there's a huge problem with having maps that are less balanced, less polished, or less competitive. Experienced players might not notice this, but new players are pretty put off by being told "Oh yeah, that's twisted treeline. It's way unbalanced and nobody cares about it." Not to mention the players that actually really like the map but are really mad that Riot ignores them because the map needs some really significant changes to be balanceable.
I don't know how you can get mad at having shoddily balanced champions and then be fine with shoddily balanced maps.