When Donald X. said this was going to be the most complicated expansion, he meant it.
This card is pulling a Mandarin . I think the on play effect is decent for a 3$, albeit terminal. I think the on-gain effect will come in handy the most mid game where you have some engine components already and you want to clear out a lot of junk at once, and you get a playable doctor afterwards. Early on though, I don't know how often I'd want to spend 5$ on a Doctor when other strong 5$ cards abound.
The problem with mid-game trashing is that there is already a fair amount of decent cards in your deck. Say it's turn 8 and you haven't trashed anything yet, you'll likely have about 10 "keepable cards" (counting an extra gain/buy here and there) and 10 trashable cards.
So on average 1 out of 2 cards from the top of your deck is trashable. Let's pay $7 for Doctor and drill down 4 cards, we can expect to find 2 bad cards, but we have to start from the top. This has been mentioned before, but let's say it's Gold or Platinum or anything else you'd like to keep. Are you going to discard them hoping to find a lousy Copper or Estate? And if you don't find anything to trash, well, you just wasted 4 coins.
In my view, the overpaying for on-buy trashing is too expensive. By the time you can pay enough for a good trashing, there will be all those good cards in the way! Maaaaaybeee a niche combo will be with Apothecary which tends to set up bad hands after your current one, like a reverse Scout. The on-buy is pretty hard to pull off efficiently.
And this just leaves the on-play effect, which I think is a tad worse, okay, maybe it's roughly even par with the better trashers at $3 and $2, but still nothing to go crazy about.
A card like this does mean there will more often be a trasher available though and that's always good.