A combo Black Market/Vault that puts the gained card into your hand immediately? That is just insanely strong.
The idea of gaining an action card that can be played immediately is very strong, yes, but you still need to discard a bunch of cards to make it work. It wouldn't be all that great unless the Kingdom had cards that worked with small hands. Those types of combos should be acceptable though!
By using the discard mechanic, it is no longer a Black Market. And I would say to keep it as Secret Chamber instead of Vault. I think it keeps it from being
insanely strong.
The trade-off I usually associate with the other gainers is the ability to easily gain more copies of a desired card in exchange for not getting to play those cards for an extra shuffle due to spending the first buy on the gainer. Conscript largely eliminates that cost, and so it needs to be inferior to the other gainers in some other respect, such as by being harder to use effectively, costing more, or both.
Well, the trade off is that to gain an expensive card you need to discard most of your hand. Sometimes this might be to your benefit (Library, etc.) but just because there is a strong combo doesn't mean that the card itself is too powerful.
As for allowing it to discard non-treasures, I think that would be a bit too strong in general, and set up totally crazy interactions with trimmed action-heavy decks; imagine throwing it into a scrying pool deck. Also this would eliminate the penalty for having conscripts collide, which I think would be a bad thing as this card may have a tendency to get spammed.
Again, having some strong combos doesn't seem like a bad thing to me. The question is if it is really so out of hand compared to other interactions that are already in the game. It doesn't sound over the top to me.