I think it would be an interesting idea if it could be programmed.

For example, Dark Janus Chess would be cool, but not popular enough to be a game in itself..... but if could be done with the intermixture idea would be cool.

For ratings, I would either make no ratings for the "intermix" games - or just make an "intermix" chess rating to cover them all - but that might not be good since I'm sure some mixes will make the game very one sided.

Tournaments should not be a problem - if someone wants to make a tournament of it, the mixture rules would be there for them to choose to sign up or not.

If it is not too hard to program, I would vote for it - but my guess is that it would take programming each possible version making it too much problem to program.