Is it just one disc that won’t play, or all of them?
An external Optical drive that plays Blu Rays should work to play the discs. Copying them to a server , or even another disc, is another kettle of fish. It might be possible but probably not worth the effort of the workarounds that are necessary.
I can’t speak for the stability of the reader in the machine vs an external reader. It probably depends on the individual optical readers and BRP. There are certainly a lot of cheaply built computer peripherals out there. I also one had a $79 Sony BRP die on me after 2 years. My Oppo 105 and 203 are going strong after years of use