Rob - rental trollies everywhere in GB&I are two-wheeled pull-carts. That’s very normal. Folks who own their carts have ones similar to your speedcart. Again, very normal. Rental trollies are a very utilitarian item... basic, just meant to get the job done. Some courses might offer nicer ones (like push carts) in a rental fleet, but I haven’t seen that in GB&I.
As for trollies in the States... yes, they have been a fixture for quite some time at a FEW places. But, trollies are UBIQUITOUS in GB&I. You would be hard pressed to play any course that didn’t offer them.