Usually the problem with support is how useful it gets in larger groups and how useless it is in smaller groups by comparison.
A support would probably be balanced around an 8 man party, which would make them weak in 4 mans.
If you required a support for each group, you'd be segregating the roles by a huge amount and queue times will go up like crazy. This may have worked with a 5 man party for dungeons, but it's unlikely with four.
You'd also have to give them enough damage for soloing, since then it'd just be hard on them outside of raids. But you can't give them enough damage or people will just stack support and they'll all buff each other into an Omega Weapon. It's really a balancing nightmare.
I like support classes. I mean, TRUE support not just subpar dps with some extra healing. The ones that manages multiple damage, healing and defensive buffs. It's just horrible to balance and players complain if they're useless outside of raids (which is reasonable).
IF, however, you could scale the balance to the party size and maybe the amount of other support (limit stacking of buffs), then it may work. However, there's already only four dps slots per raid(calling 8 mans a raid, bite me) and 2 per dungeon, so this may divide the roles too much.
Support works better with bigger groups.