How can I win without using broken champs?
TL;DR, the title.
As for the long version... I enjoy playing champs that are more mechanically complex. Ones who don't just click people to death or spam one button into infinity, champs with interesting abilities that are just "push button to do damage" or something like that, and so on -- But, it seems like my enjoyment of harder champs is the main thing holding me back from ever winning any games.
So, basically, how do I win a game with a harder champ against a braindead easy champ that for some reason instantly kills people?
Say I'm using Azir, and I'm against someone like Katarina, Teemo, Diana, etc. I can do everything in my power to poke them and kill them, but they would just take next to no damage, easily dodge all my abilities, and then proceed to click on me with targeted abilities / auto attacks and instantly melt my face off. Even if I don't die, I'm effectively barred from farming at all, because even being in my soldier AA range, they can easily get to me. If I'm not playing someone with super long range like Azir? Well, I can't even farm. If I go anywhere near my minions, I just instantaneously drop dead, even in the early game. Late game, I can't do anything, even on a tank, because I just instantly die to all the braindead easy champs.
How can I fight someone who out-bursts me, out-sustains me, out-pokes me and has no resource costs for the majority of their damage? : /
Now, when I play these easy champions, I do very well. On my first game with LB, I went 19/2 and absolutely destroyed everyone. On my first game with Yi, I went 14/5 and helped every lane win. On my first game with most of these easy champs, I just absolutely carried and won games... but I just didn't have fun; the more mechanically complex champs are fun for me, while the easier ones are just plain boring. Even though I won, it just didn't feel like I really did anything to deserve that win.
Is there any way I can compete without using the broken, boring champions? I'm just tired of losing ranked games (I've lost 9 series in a row), but I want to have fun while playing the game. I just don't know what to do anymore.