That is right, which is why the whole notion of degradation of genes is poorly defined. What you are saying with stability is different. It has better definition, but still suffers, as @Mercer has explained.
As for @Rumraket clarifies he means there is about. 65%-70% chance that a muation will reduce stability in a folded protein. I don’t object to this. That is essentially 50/50, and it is self limiting too. Unstable proteins are more likely to get a mutation that increases stability. I had thought he meant that mutations that increased stability were exceedingly rare (that isn’t true).
If you keep negative selection in mind, we expect that proteins will remain as stable as they need to in order to work. I’m not seeing how this is a problem for evolution.