Being good at this game just takes a good understanding of the mechanics. It doesn't necessarily rely on being 'good with a character' or 'bad with a character'.
I do recommend trying to narrow down who you will play to just a few champs, but only because getting a strong understanding of one character and how they fit.
But you want to understand mechanics like how to kill minions effectively, but without pushing your lane. How (and WHEN) to harass your opponent in the lane and how to avoid their harass yourself.
And then once you are good at all the things that you are individually responsible for in a game you have to learn and implement the things that are important from a team aspect.
But I guess the point is that you want to focus on understanding the game. It's fine to have a poor individual performance while you are learning as long as you are learning stuff from your games.
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Eff_Dee