This is also being done. Micro-reactors are generally sub-20MWe and are intended to be portable. The biggest name is micro-reactors is probably Project PELE[1]. PELE is a DoD project to develop a trailer mounted micro-reactors for remote deployment.
PELE will be tested at the Idaho National Lab[2] (DoE's primary nuclear energy research lab). Speaking of INL, they are also building the MARVEL[3] reactor. MARVEL is another test reactor of the micro-reactor type. MARVEL is being funded by DOE-NE (if I recall) and is designed to be be a 100kW.
One use of 2-3 years. You have two of them working at the same time and when it’s time to refuel you have a new one waiting and old gets shipped back to factory for refueling.
The expensive part of nuclear power plants is all the electricity generation part (turbines/generators/piping/transformers/etc) that is pretty much the same as for coal power plants. You don’t swap out any of that.
They are the size of a shipping container, not prohibitively expensive to move. The customers buying these things have no ability to recycle/refuel or dispose of the spent fuel. I presume any purchase agreement comes with a commitment to deal with it at end of life.
I guess if the supplier goes out of business, you might have trouble, but I'd expect these companies are putting things in place for that eventuality e.g. insurance.
They are one-use batteries in the sense that they are sealed and not intended to be refueled at the place of deployment, if ever. They can last for a decade without refueling though, so it may be fine.