It doesn’t matter how likely any individual mutation is to increase transmissibility or resistance. We won’t ever see the ones that decrease transmissibility or resistance, because they’ll be outcompeted by the Brand X virus, as well as any nastier mutants.

Then why has it taken this long to see a global pandemic? Surely it must matter to some extent how likely any given mutation is to increase transmissibility or resistance.

That's probably random, but the mutations that increase contagiousness will be the ones surviving natural selection.

I recall a general principle in virology that given a virus found in the wild, the more contagious it is, the less harm or death it causes. (If it killed every host it would have no long-term survivability)

Most mutations probably just render the thing unable to replicate and it "dies," much the same way flipping a random bit is more likely to cause a program crash than do anything useful at all.

The relative rate doesn't matter, the absolute rate does (how often does it mutate at all and survive to infect another host).