I was thinking of this same issue myself since I have an itinerary coming up in June with changes on the order of 15-20 minutes in the departure/arrival times on most of the flights. Luckily, no connection times are blown by the changes.

I think the problem in execution isn't necessarily for clicking Yes, the changes are fine -- obviously. It's what to do if you are NOT happy with the changes (or they will make your connection times non-viable). That is where the complexity lies -- in rebooking or cancelling. Obviously, it's doable, but not nearly as simple as where you just accept the changes.