I like it, but I think it has some unintended consequences.
With enough coin to buy 1 copy, and enough buys to buy out a pile, you can insta-pile anything (except potion costs). Buy something, trash it to this, then buy the next one. It will make for an unexpectedly quick empty province pile.
You probably need some errata about coins on other player's turns, just in case Embassy or Messenger is on the board (or even Ambassador).
The rats combo is crazy good, and it makes cards like University, Altar, and Ironworks extremely good, and Jack of All Trades even better. It also works very well with Remodel and its ilk, turning it into pure trashing plus bonus coin.
I like the concept, but I think this is a little too powerful. That being said, playtesting will usually give you the best answers.