How many people do you run across who troll from the very start? In my experience it's actually quite rare, with most of the trolls I find deciding to troll after something happens in game instead of in champion select.
As it is right now dodging because you do no like someone's pick is punished, and in my opinion that is how it should be. Under a vote-dodge system it would be the person with the unconventional pick who is punished. No they won't lose LP for it, but how many games will they actually get to play? I've honestly seen more people apologize for giving another player a hard time over their pick after they carried then people who pick out of order or decide to be useless while in champion select.
In my opinion the good part of a vote-dodge system simply does not outweigh this. Riot should be focusing on removing trolls from the game instead of adding unnecessary and abusable things like a vote-dodge mechanic.