We are on the same wavelength here!

Pretty well everything you say is true, it's just the behavior is somewhat more random than you would think.

Yes, all else being equal, in the long term fearsome killers would tend to become mostly harmless bugs that would coexist with humans.

But there are many confounding factors in the medium term.

For example, in COVID, the spike protein is what makes it so successful. It might be that there isn't actually a plausible mutation of the spike protein that is lot less deadly, but still usable.

Also, because a successful mutation is literally one in a trillion, there is considerable luck of the draw involved, and this only gets mitigated by the law of large numbers over a fairly long time.

Consider the vastly huge phase space of "all genetic patterns of or near COVID-19" (waves hands a bit here). 99.99999% of these are nonviable, so we color them black.

Scattered randomly around this space are a small number of viable areas, so we give them complicated colors depending on how infectious it is, how long the incubation period is, how fatal it is, how well it gets past the human immune system.

Now "COVID as a whole" is wandering blindly around this huge phase space. Each COVID-19 virus mutation starts in one of the lit up areas, but nearly always, takes one step and falls into blackness and dies.

Occasionally, a step leads to COVID a fresh lit up area, but which area it is and what "color" it is is "indeterminate".

Once COVID does get into a new lit-up area, there is a hill-climbing effect that does tend to make it converge on a local maximum (because "small" mutations are more likely than "big" one).

So in the medium term, there might be huge surprises yet. In the long term, you would expect COVID to end up like the flu. That still sucks.