As Bester has said, my understanding is that it is designed in the way it is, so that all of the promotion seminars can take place before the pre-season begins and then the newly promoted officials (at the higher end of the spectrum) manage to get a few matches worth of experience under their belt before the start of the new season.
Going back to the point about the seminar's, the Football League and Premier League seminars (PGMOL) can then distribute kit and run fitness tests for those who have been newly promoted without interfering with the start of the season. In general it gives more preparation time for those who have just been promoted. To be entirely honest, I would much prefer it this way, than the promotion season end in July, not find out until August who has been promoted and then have to inform my leagues whether I have been promoted as the registration forms would have already been sent in.
The same above applies for Supply Leagues. Having level 5's register to their normal leagues, then to find out in August that they have been promoted, then fitting a fitness test in whilst pulling out of the other leagues they have signed up to, would not be practical.