I'd rather see FA start before, but I get they do it that way to give players who was just in the finals some time to process. IF this went to game 7, it would have give everyone 5ish days to process win or loss then if they are statying with their team, and if they lost they may bolt. It's only a week, but it's a big deference.
Can't really go later with the draft, kids need to move, get to summer league, and work on learning the system. That extra week is big too.
F it, same day, draft and FA. Start at 8am est, all owners and GM's in NY at the same time battle royal!