Except in the case of Covid the host is contagious before symptoms develop, so there is no evolutionary pressure on it to be less deadly (i.e. give itself more time to spread by not killing the host).
It is common for people to become contagious before symptoms. But contagiousness is not a binary on/off switch. As your virus load increases, you get others sick more easily. And the result is that most people continue to become more contagious as they develop symptoms.
But there is also a second factor. We have multiple layers of immune defenses. COVID is very good at getting past our initial defenses and getting us sick. Over and over again. But if you've had it once, you have the ability to ramp up against it quickly in a way that limits how sick you can get from it. So if you've ever had it, it is now much less deadly for you. (Unless you become immunocompromised.)
Evolutionary pressure doesn't factor into this. Imagine the virus doing a random walk over a bell curve of virulence. On average an outlier is going to mutate into a not outlier.
SARS-1 was an outlier, very deadly. SARS-2 s probably not an outlier.
That said I think a virus can evolve to the point where it's arguably a different virus in which case the median virulence can change.
