I'm inclined to believe that the delivery windows were designed as so they could be bracketed ordering waves. Essentially, I expect most people in the 4/24-5/8 window will get them on the 24th, and then we may see very few deliveries for the next week or so, and then another wave of deliveries begin in the next bracket, or maybe even a day or two before. By creating these windows it appears that Apple has designed a wave system based on their confidence in current supply plus manufacturing.
My guess is that the initial delivery window comprises of the supply currently on hand, and nothing more. If that's the case, there isn't really a good reason why it would not be delivered on the 24th. All future waves are likely determined by Apple's production projections going forward from the initial wave. With any luck Apple will continue to improve the manufacturing process over the coming weeks and those June and July orders will bump up by a few weeks.
Again, I understand that Apple has stated these delivery dates to be what they are, and that we cannot EXPECT any more than that, but we can still make predictions based on logic and the limited information available to us.
I'm not doubting that and I do hope I'm wrong. That said it is all assumptions for now until there is actual change in people's delivery status.