Yeah, I agree with dragonbird. You have to posess magical talent in some degree in order to become a sorcerer (Yennefer tested Ciri for it; she knew Ciri could learn magic because she felt energy in Yen's necklace or something like that), but it seems this trait is not uncommon, just commonly unexploited. The same way many people could potentially become musicians, mathemathics, painters and such, I think. You need talent + studies + practice. Sorcerer as a profession has a bad name though, but still allows you to earn huge amounts of money, so upper-class people send their malformed, un-marriable children into sorcery school.
I suppose there are people overwhelmed by their magical talent too. Like, possesing a great amount of power but little intelligence, will to tame it, or just lacking the opportunity of someone to teach them, thus becoming crazy, catatonic, etc, like Tissaia wrote. I think Cedric may be an example of this. I doubt they actually forced sterilization in the young adepts. Most of them were going to end up sterile anyway.