Not so.
Firstly, broadcasters typically won't care when games are played as long as they get their full 38-game season and their full quota that they've pre-sold to their viewers. If the seasons are adjusted, the transfer windows would too.
If you look at players contracts ending on the 1st July, assuming the season would still be running then, there would be no point in those players leaving the clubs because they would have no other clubs to go to.
It would be a very simple exercise, probably led by the PFA, to extend contracts for the short-term under extenuating circumstances. Clubs up and down the country do 3 and 6 month contracts with players all the time.
So it really only boils down to traditionalists wanting to stick to Aug-May without good reason. You say that Football fans are 'notoriously resistant to change' and yet we largely accepted goal-line technology, female officials, changes to kick-off, changes to offside rules and now VAR. For those that haven't accepted it, they've been power-less to stop any of that anyway.
Times change and Football will adapt.