The lack of overheal really hurts it. I think you're right that allowing it to overheal during ubers would go a long way (particularly since it would be much more useful against sentries).
Speaking of the medic, that class could really use more stuff. And this isn't because my #1 class is medic.
The medic, engineer, and demoman are sort of victims of their own success - it's hard to give them equipment that's worth using over the vanilla stuff. I imagine this is why nearly all of the demoman unlocks are for demoknights, the default sticky launcher and grenade launcher are hard to beat.
I knew it! I kept saying mine was broken and people thought I was making it up or something. They also said things like "maybe they finally fixed it?". I don't see what people don't like about it. It's one of the better additions to the game if I had to pick something that doesn't make me rage. (Like the Huntsman, Phlogistinator, plus others.)
I think giving it a bonus against spy checking
and silent kill is too much. If they really want to give it so many stealth bonuses they should balance it by taking the spy's offensive capabilities down a notch - say reduced revolver effectiveness. Although I think the best fix would just be removing "silent kill." However you're right that a good pyro is unlikely to be fooled. I've been killed by several spycicle spies, but I've toasted far more.