You have choices. If you pick up a high skill champion, once you learn enough of them, you are able to carry more games through sheer microplay that is not available on the lower end. They are less subject to the whims of their team, or situations created of them.
Now, there are middle ground champions who are relatively able to showcase a skill ceiling, but aren't that out of reach for quick pickup. An example is Renekton, who is conveniently very strong right now.
So, no you do not need a high skill champion, it's just if you learn those mechanics, those kind of champions can turn many situations which seem too sunk otherwise. These generally tend to be the champions smurfs use to climb, because it's more consistent to outplay opponents even when you're in a normally disadvantageous situation.
Alternatively, you can play the lower skill champions, and learn some macroplay and lane dynamics, and also climb because the basics are incredibly important and many people lack a holistic understanding of them which gives you a good edge through at least Platinum area. These also transfer to high skill champions and let you use them far more effectively in many cases, although depending on balance, not always the case.
Up to you, just know that it is not necessary. Play what feels comfortable.