For me, the trick is to guide like a mouse, not steer like a car.

The only place around me that has 4x360° wheels is IKEA (i.e. occasional-not-frequent destination), but I prefer them generally to the standard-issue sort.

It really depends a lot on the upkeep. If stores do no upkeep then in no time you end up with carts that all have one wheel clogged with hair and pulling the cart steeply to one side. With regular maintenance you have smooth running carts that don't have any directional bias and are a pleasure to use.

A supermarket local to me had stickers for a while you could grab as a customer and stick on a cart if it had a stuck wheel. They'd then take that cart out for repair. They don't do the stickers anymore, but I figure they just keep on top of keeping the wheels running smoothly nowadays. Haven't had a cart pull to one side in years now.

I don't like them either, but hardware stores and Colruyt (a Belgian supermarket) have four pivoting wheels but also a fixed wheel in the center under the cart, which allows it to turn much more easily. Those are great.