Firstly, I think it's strange that you are referring to them as a "Villain". It puts a negative light on them before you've even described anything. Something like "opponent" is neutral and more accurate. Throughout this post you make loaded statements and questions.
Secondly, you speak of your "very strong engine" that can generate 3+ provinces a turn. This is a strange statement to make, especially seeing as your opponent has just made $30 and 4 buys. That sounds like a pretty strong deck to me (after all, it can gain 4 provinces!). At any rate, the quality of your two decks is completely irrelevant to the discussion. By including this statement, it makes you sound as though you just think you're better than them.
I would both grant and ask for this undo in a heartbeat. If you actually stop to think about what they want to undo, they want to keep a single gold in their hand to enhance it. They're still planning on buying 3 provinces, they just want to keep a card in hand. There is no information gained from this undo, which is the criterion that most undo-deniers seem to use. It seems highly likely that they just clicked Autoplay treasures. It's happened to me plenty of times where I meant to keep a card in hand but my brain just went on autopilot and clicked "autoplay treasures". In those cases I don't always catch the mistake immediately since I'm trying to not be unbearably slow.
The experience of Dominion is, in my opinion, improved by the ability to undo. In addition to misclicks, allowing undos for straightforward things such as this lets people play the game at a faster pace, without having to painstakingly stop for every card to just to make abosolutely sure that there's no reason they'd ever regret it. If you spectate high level play, you'll see that undos are almost always granted and there's basically never a fuss about it.
This whole anti-undo philosophy really gets on my nerves. People act as though it somehow detracts from the game or makes it less fun or pure or something, and it always seems to come from a perspective of the people asking for undos somehow being weaker or less deserving. People make mistakes, that's why undos exist. Letting your opponent undo a few simple things is just a nice thing to do, and denying it isn't going to make you a better person.