That's an interesting idea.... Allow them to buy skill groups based on a training mindset for particular backgrounds. I like it!
It'd definitely be a house rule to put in place for a theme character/game. And you'd have to watch to make sure you don't go crazy with it*. But it could definitely work. I might not call them Skill Groups, but maybe "Career Groups" to set them apart.
A Doctor group could contain Cybertechnology, First Aid, Medicine and a choice of an Academic Knowledge (Biology, Pharmacology, Anatomy, etc.). Or a Demolitios/Bomb Squad group containing Chemistry, Computer and Demolitions. Of course, Espionage group containing Forgery, Unarmed, Con and Survival.
*By crazy, I mean somebody would bound to suggest a Shadowrunner group containing Pistols, Dodge, Con and Computer just so they could max those skills for a pittance.