Playing all the champions is important to climbing.

Its true, usually the difference between a diamond or platinum player vs a silver player is not "skill". Its knowledge of strategies to use.

1. In a 1 v 1 let me go into the bush and auto attack him so I get an advantage
2. Let me farm all the creep minions *
3. Know which abilities cross minion waves and which dont
4. Let me play some of the broken champions/ counters

SIlvers and bronze dont play the game enough to know all the champions but if they read all the rules and tips, I have no doubt in my mind they can climb easier.