I generally dodge if I get a garbage champ. I don't care if I get a dodge timer since generally I will only do it once or twice and after that stop playing league for the night so it does nothing.
I am not gonna sit in a game as Tryn or Yi and be useless, not happening. At least if I am someone I can build as a tank and eventually be useful, or my team is a lot of god tier aram champs, but otherwise screw that.
I will also dodge if the team is all tanks or all melee, not dealing with the enemy poking us to death. Since it always seems like if we get a garbage team, the enemy will have Velkoz, Lux, Ashe, Jinx, Ez, Nasus, Nidalee and such.