I understand the reason for DL making this change and it will effect flyers in different ways. When I am travelling for leisure to Europe for a week, and there is a 2 hour change with an additional hour at my connection, I shrug and say who cares. However, when I am going out and back for a meeting in the same day, 119 minute shifts on the outbound and return can result in serious issues. Even with the 90 minute rule, there could be issues. Fortunately, the couple of times that happened to me, DL has empowered staff to do what helped rather than follow things to the letter.
Overall, I think this is a non-issue for the vast majority of DL flyers. Joe Sixpack heading out for his weekend vacation is not going to have his vacation ruined if he arrives 2 hours later rather than 1.5 hours later. The Flyertalk road warrior that is scheduling an itinerary down to the minute can get DL to refund a 91-119 minute change if it truly effects the purpose of the trip. It should also be noted that with any change, you can request something different.
Going back to the barber analogy, it would be more like the barber says he cannot do 5:00 anymore, but can do 3:01 or 6:59. If neither of those work, he'll put your money on a voucher you can use later, but the price for the haircut may change.