To my credit, I've only been a spectator on that thread of late. I was addicted back around December, and relapsed briefly a few weeks ago, but I've been clean for a while and I've never felt better.
Here's my only attempt at a logical explanation for restricting push cart usage: If carts are at 90*, or restricted to paths only, then perhaps there's reason to fear that if push carts are allowed on the turf their wheel tracks will be visible and will lead to cart drivers following the lead after assuming that other carts are off the paths. It's a stretch, but my club doesn't allow push carts at all and we still can't keep carts on the paths no matter how many signs we put up. If there were wheel tracks going straight through the moisture down the fairways, I have a feeling the carts would follow.
But let's be honest - they're just trying to collect more cart fees at a time when it would otherwise be more convenient to walk and push. #MythBusted.