They can, they just usually don't, as more dangerous viruses kill their host before they can spread as far...

It's wrong to say they usually don't, it's that the deadlier variants haven't lived long enough for us to remember them or have to worry about them at this moment. They still happen and can wipe out populations, and thus die out, as well. They can also reach an equilibrium where they maim many of their hosts, more than we'd like, without killing them all.

Mutations are random, nothing really is preventing a virus from replicating rapidly and killing a lot of its hosts in the short term, it's just the long-term evolutionary advantage of such traits are small, because killing hosts quickly reduces replication, potentially.

But that doesn't stop viruses and bacteria from mutating into something deadly and killing a lot, or all, of its hosts. However just that has happened throughout evolutionary history on Earth, and even in humans' history. We've seen plenty of pandemics wage war against humans and cause considerable casualties.

There's also plenty of equilibria deadly viruses can reach with their hosts, where they kill a relatively large amount of hosts, but not enough to wipe them out.

If mutations are just random then why do viruses ever reach equilibrium?

Sometimes this can be an effect that causes viruses to mutate to be less virulent.

On the other hand, faster replication is also often selected for, which often corresponds to more virulence.

Both trends have been observed, depending on a whole lot of complex factors.

It can and does happen: https://en.wikipedia.org/wiki/Influenza_pandemic#Influenza_p...