It's because Support in AO terms means "Has healing other capability.", which is why its just Fixer, Doctor, Keeper, Martial Artist, Meta-Physicist, Adventurer, Trader as they can all heal their team mates to some degree. They didn't count FP Agents I because that's only in FP and not by default.
Or in short...
Support: Heal other people
Control: Pet classes & tradeskills
Artillery: Damage dealer with ranged
Infantry: Damage dealer with melee
Extermination: Damage dealer with nukes
Its semantics based on the language used, control isn't anything to do with crowd control really for example. So if you look at it like that it makes perfect sense?
Not saying loosening up the req's isn't a terrible idea but all I can see it doing is every prof will use exactly the same symbiants across the board and any symb that isn't the best in that slot will be completely pointless. I'm not sure going that way would be any better. So... in short you want 10x more worthless junk symbs looking for the few good ones or keep things spread around like it is now? :P