This isn't guaranteed, there are plenty of viruses that are still cause severe illness despite being around for quite some time. It's entirely possible that the virus mutates to be more lethal[1], as well.

And if mortality does decrease, it could take many human lifetimes before such an equilibrium is reached. In the meantime, the virus can mutate, wreak havoc and kill a lot of people.

It's also important to point out that virus evolution depends on selection pressures, and one of the selection pressures for decreased viral lethality is a severe reduction of host organisms that the virus can replicate in. That is to say that the selection pressure that causes a virus to be less lethal can very well be the eradication of large populations of host organisms.

[1] https://www.usatoday.com/story/news/factcheck/2021/07/14/fac...