The hate being picked up in general, even if there is no threat of vet, so they’ll struggle to get out of my arms and if they succeed - I’ve lost the element of surprise.
Also - I have two cats, and if I need to take both to vet then even if I manage to place one in a carrier he’ll alert the other that something is wrong.
Just how docile are your cats? If I’d take my cats to the bus without a container I’d have to run back and forth trying to fish them from the overhead storage racks when I reach my stop.
I tried releasing them in my car once, and they managed to squeeze under the driver and passenger seats. At least that was an environment fully under my control.