No, they can't. If a consumer has no contract with a game producer, then he can't. He can't dictate CryTek to make RPGs, he can't dictate Crystal Dynamics to make a side-scroller, he can't dictate DICE to make iPhone games. He can't dictate them to make the games accessible to the blind, which would actually pretty cool, I would love to hear high quality aural games.
Particular developers don't even go to the market and ask people what kind of game they would like and then do that. They just make the game they are either familiar with making, or they want to make for "personal" reasons.
In fact, lots of games come from individuals thinking about it for some time, and manage to find a sponsor to produce it, when the sponsor thinks it's marketable.
Monster companies like EA might look to the market and think it's time for another RPG, and then put one of their studio to do it. Which in effect might end up boring because of it.