Sure, but that just implies most natural proteins exist in some zone of stability above too unstable, and below too rigid. But apparently mutations towards higher stability are less likely on average compared to mutations towards lower stability. It is true that stability increasing mutations are not necessarily function improving.
The key point is that in general, if proteins lose stability and go below this zone or “threshold of stability” with the highest fitness effects, it negatively affects their function. And some random mutation is initially likely to be neutral because the protein is in this “threshold” zone where it is somewhat buffered against the stability-affecting effects of mutations, but invariably mutations do affect the stability, and are more likely to be downwards than upwards, so after a few mutations have occured, it is on the border of beneficial stability (most likely downwards towards more unstable), and will become function-affectingly unstable with further mutations. Again, in the absense of purifying selection of course.
I’d point to the work on P53s to show that it is about 50/50. The studies you are showing are not measuring stability, they are measuring function, right?
Well it depends, the study I linked above is essentially a review and theoretical discussion based on lots of different empirical experiments. Some of which measured stability, others measured function as a proxy for stability. I think you have to read the paper to get the full picture. There’s this figure which does a pretty good job of explaining it though:
