Yes, that would be better, for specific instances of the running program to have a set of permissions instead. However, I think this is not the only issue.

It is what I had wanted too, not only you.

I think that the entire operating system should need to be redesigned for many reasons (I mentioned before how to design a better one), and it would have that effect, that specific instances of a running program would be given capabilities as arguments (or through other capabilities, but the first ones must be given as arguments), and these capabilities can have restricted permissions, as well as more versatile things e.g. to log access, or to go through a proxy, or to set a disk quota, etc.