One trick ponies, is it faster to climb relying on one champion or 2 and 3?

There's a reason I stopped using Annie in all my games and started to use a bit of Cassiopeia . To avoid counter picks champions that are incredibly strong in the meta: Orianna , Lux , Syndra , and Xerath , just to name a few. This way, I can go even if the matchup is no longer in my favor and still take out most assassin champs with Annie.