Well i might see your point about the support but i disagree with the jungle part, in fact i would argue that her design pushes her to the jungle, mediocre early game that's still better then eves, Mana hungry on her primary poke max of Q, and W cast disrupts autos and have a noticeable delay before the heal.
Her E is excellent for clearing camps so long as you use it properly, W is a good 1-2 point wonder, and Q is great for aoe damage + increasing slow for ganks / disengage since she can cast it while moving.
If your seeing kayle do bad in the jungle its due to A. reworked champion muscle memory syndrome, B. The horror show that is her "recommended" jungle item page, it actually recommends red health pots, and suggests the attack speed jungle item on a very melee range champion instead of runic, it doesn't suggest
and ignores solid defense options for a champion of kayles range difficulty's like
and not even a mention of 
One thing i can say it would be terrible to have the rioter that made her jungle page on your team with the recommendation to rush
right after finishing
you would get a jungle kayle that consistently dies the moment anyone looks in her general direction.