They work until they don't. The old simple Dometics like you have are very robust and can last and last and last. I would not replace it until it dies, but when it does I would replace it rather than attempting a new cooling unit.
I replaced the one in my Argosy about 4 years ago, only because I wanted a larger refrigerator. The old one was working fine, and in fact I have it still in storage.
I sold a 1971
Caravel last year with a still working original refrigerator.