Having an invisible trigger condition begs for problems to come up. As the game goes on and players buy multiple Stashes, your rewrite requires them to keep track of how many are in their deck at all times. This becomes too much of a chore with trash cards, Masquerade, and just buying multiples. Say I've purchased a Stash and trashed it long ago. I could easily believe I have one left in my deck, believe the trigger is occurring, search my deck, and find nothing. Did I make a gameplay mistake, or was I getting advanced information about the remaining contents of my deck?
Invisible triggers are dangerous like this. No one wants to be accused of cheating for these little mistakes, and no one wants to feel like someone else is cheating because of a loophole. And then you have the people who will cheat because of this. It's not worth it when an interesting alternative is available.