Riot, if we miss a pick or ban, can you at least let us play Dominion/ARAM/TT/Bots?

I understand, to a degree, the point in treating missing a pick/ban the same as a dodge in the new queue, but CAN YOU PLEASE AT LEAST LET US QUEUE IN A DIFFERENT GAME MODE? Like, I get it. I really, truly do, but some of us didn't intend to not lock-in a pick/ban. Some of us maybe had some ping hopping or latency issues happen randomly. Some of us may have been delegating with our team on who to pick/ban.

Can you at least open up the opportunity for we who missed the pick/ban to queue into another game mode? Maybe make it a deal where anyone faced with the same situation is allowed to queue into a different game mode, but after X amount of dips from the Draft queue we are no longer allowed such luxury.