My honest opinion (if incorrect answer): it wouldn't be much different at all.
I play a rota of courses all with 'terrible' bunkers -- one bunker is very wet and mushy, the next one is like hardpan, the third must be under repair, the fourth sees a lot of play 'cause it's all churned up, the fifth is 40% standing water, the 6th they must've just backed the dump truck up the day before 'cause there's mounds and mounds of dry fluffy sand, the 7th is hardpan and pebbles etc etc.
I'm not a great bunker player and never practice, but I adapt, hole by hole and bunker by bunker, trying one technique here and another one there, a sand wedge out of this bunker and low bounce 52 degree out of that one, sometimes hitting a good couple of inches behind the ball and sometimes trying to nip it clean etc etc.
And if I can do that anyone can - top amateurs and pros especially.
They would've adapted very very quickly to a rakeless world.
Now, if there was nothing but 8 foot deep and 10 foot around sodfaced pot bunkers, well that's a different story! Plop those down and next to the greens at a regular PGA Tour stop and you'd see strategies and playing styles change very quickly.