In my experience, it seems that not granting an undo is more likely to spoil a game. I think the feature serves a legitimate purpose to fix mis-clicks, or work-around bugs or difficulties with the interface.
I’ve only had a few opponents request an undo, and I don’t think any of those cases involved a player abusing the feature to cheat. I would not want to unfairly win from my opponent mis-clicking, hence I am happy to grant these undos.
I’ve requested undos a few times as well. These have all come about from either: making a misclick (on a touch-screen, I’ve even managed to do this with the submit move button) or the UI issue mentioned above.