It would seem a bit impractical.
Drops, marking and replacing the ball on the green and picking it up out of the hole would be a right royal pain in the backside if only one person on each hole can do it.
In fact it's impossible really regarding drops.
Then on each tee they have to remember to use their own ball.
Given the courses are full at the moment I don't think alternate shots is practical as they'd move quicker and so there's an issue trying to get through groups. Yes I know people should move aside and I would ensure my group did but you know there will be people saying "I'm the 10.30 time and there is nowhere for you to go" We don't play alternate shots unless it's a competition as a rule but I know some clubs do have certain days/times when this is the preferred format