I really like him as a player and will miss him, too, but his hesitance to shoot is far from his only flaw on the ice (I know you just said biggest complaint, just expanding on that).
He's not fast for his size and he is surprisingly ineffective on the powerplay. I'm not sure why, he always seemed like a powerplay monster in college and showed flashes of it early in his career, but over the years, it's like he just lost all of his assertiveness and creativity on the powerplay. Due to his lack of size and speed, even if he wins a puck battle, he sometimes can't do anything with it because he's still boxed in on the boards and can't escape checkers or make a move to the inside. So Schwartz will sometimes go several games in a row where basically all he does is jam for the puck along the boards in the neutral zone and fall down. He also has no idea how to screen goalies. He always drifts to the side so the goalie can see just fine and he makes an ineffective attempt at a deflection.
If he played around the net the way he does on the boards, I'd want the Blues to give him a blank check.