Indeed. I never memorized anything, then I got to uni. It's just a waste of time rederiving 5000 years worth of mathematics for the fun of it, and pretty much impossible to do in exam conditions. You need to know the theorems backwards in order to be able to intiutively apply them.
It's exactly the same as how basic calculus is taught...integration at low levels is a HELL of a lot easier when you know that say, 1/n integrates to ln n, and you can then just use basic algebra to get your integral into that form. Without having that core intuitive knowledge obtained by practicing and learning, you can't make those jumps.
I strongly disagree. It does make you such. Memorization is overrated.