Maybe it's just me, but if weekly free champions is a problem in ranked games, banning them from ranked games wouldn't be too crazy. After all, presumably in a ranked game you should actually know your champion and be pretty good. Since you get ranked and all based on how the game goes.
Whereas in normal games, you win some, you lose some, and it really doesn't matter much either way within a minute of the game being over. That is why people play multiplayer games after all - because winning all the time easily like most single player games offer tends to get...repetitive.