Does vaccinating the most vulnerable world-wide actually reduce mutations?

In fact, pathogens tend to evolve towards less lethality, for the simple reason that dead hosts don’t spread the virus. Though baseline covid already has a low enough lethality that there’s very little pressure there.

Also, covid is contagious for a day or two before the host gets sick at all. So there’s extremely little pressure on it to be less lethal.

This is all true but my point was that mutations may mean that some variants may be more severe or milder than others and there is no reason to expect that the process of mutation will tend towards “more severe”.