Fuck the Wizard, save the Cleric.
Support classes are OP by nature. If Sayaka had realized that and played more Healtank than Paladon't, Madoka would have been a very different anime about Homura and her army of Healbots.
If you can only heal yourself, are you really a support class? Maybe the movies changed some things but I don't ever remember Sayaka healing anyone else (her wish notwithstanding).
IIRC, the games, which are considered largely canon compliant, gave Sayaka what was effectively a paladin's lay-on-hands.
But no, in the series she only ever used her natural regen abilities. Again; she was playing more of a berserker-type than a proper paladin, or a medic, as would have been most useful. None of the other girls have any healing ability at all, I think, which makes Sayaka best suited to playing medic. The fact that she can also play tank only makes her more suitable as a medic; everyone shoots the medic first after all. Sayaka is also very fast, which means she's basically perfectly built for running in and grabbing a downed melee or short-range fighter and dragging them back behind the lines, healing them back up, and then repeating with another. If she gets hit, she can just shrug it off. If she has to fight, she has decent fighting abilities. But it's not like Mami can do much more than bandages, Kyouko would be completely useless, and Homura probably has a bank of first aid kits and a lot of experience but no actual abilities in the field.
Sayaka was actually a really well-built paladin. The major issue she had was 1) Fighting with the Chaotic Neutral Thief, 2) Playing as a barbarian rather than as what she actually was specced as, and 3) Being Lawful Stupid.
I mean, there was also the whole "Soul Gems are actually awesome" thing but I think that's a cultural issue. I bet the incubators in America divulge that information as a positive before the Girl actually contracts.