The fridge rolls out into the room on its own wheels.
Meanwhile, with the exception of ice makers/water dispensers (1/4 PEX), fridges don't have to deal with hoses for the most part. So much easier IME.
That's so they don't tip forward when a rack loaded with dishes is pulled out. There's a fair bit of forward leverage in that weight distribution.
So I'd say they face the same kind of issues.
Washing machines, on the other hand, tend to have a brick in the bottom to stop them from walking around on their own.
(periodic recommendation: if you buy a Miele, you will pay twice as much for several times the expected lifespan of a cheaper machine. My parents have a Miele dishwasher that's over 30 years old.)
I just changed the casters on my 42U rack, without moving (or shutting down) any of the machines. Now that required some deliberateness.
Worst was sourcing the parts though. Getting the thing out, effectively getting it up on blocks to run it and see the issue was hard work. Getting the specific totally non-standard o-ring size out of the manufacturer was impossible. In the end I resorted to siliconing but I just cannot dump something like that over a 5c part.