Tree has the best winrate of all heroes. Irony?
Sven can't be kited because he kills people in three hits. If you survive more than a few hits either you got ridiculously fed or he's an idiot. He gets a battlefury for FREE which means he can farm the jungle with ease naked. Means he can play support early game and very easily transition into a carry late game when he starts farming for carry items. If you want to call that a role, then there you go. He's a carry that doesn't need farm in his early game lane.
I also agree to not play AP if you're looking for a fair game. AP was the joke mode of DotA1, no one I knew who played competitively ever played AP. It only caught on in DotA2 because it was the only choice. Play RD or SD and you will have a better time. If you really are better than the people you get matched with, pick a hard carry. If you have a new friend with 0 games played so you get matched with far worse players, you will notice it is a LOT easier to win if you pick Luna than if you pick Tide. It's the same in all MOBAs, the carry is just too important to leave to the worst player on the team. Supports are replaceable and, honestly, if the carry gets farmed enough, entirely unnecessary.