I'm a Talon one-trick (well not fully one-trick, I play lots of Zed too, but still). As such I can tell you that one-tricking a champion is a rather effective way to climb provided that you can play said champion at a higher level than you are currently at.
There are a few advantages to playing one champ for most of your games. First off, you quickly learn all the matchups. Secondly, you learn the ins and outs of the champion in basically any scenario you can find yourself in. These can help you carry even the toughest of games, or win even the worst of your lane matchups just by pure skill/experience difference.
The problems are rather straightforward: if your champ is banned you're kinda screwed and if it gets nerfed and becomes very weak you might not be able to effectively climb with it anymore. This is why nearly all one-trick players pick off meta champs that they enjoy, so that they have no risk of the champ getting banned/nerfed and they don't grow tired of playing said champion either.
Honestly one tricking is pretty good if you're able to make it work. In other words, if you're gonna be a one trick with champion X, you'd better be the best champion X player any soloq player might meet at that elo, so that you can outplay them and crush them and their team without troubles. If you can do that with a champion you like, you can surely climb as a one tricker yourself :P