I think it is the other way around, there is no pressure to maintain a high severity as long as the virus can spread thus leading to mutations that lose the severe traits.
Viruses aren't trying to kill their hosts, they're trying to replicate. But to replicate they kill the cells they're in.
COVID's severity is because it's making a tradeoff between the time it takes the immune system to destroy it, vs the need to get a host walking around and socializing while breathing it out onto new hosts. The lethality is a side-effect of its replication strategy.
Viruses lyse (explode) the cells they take over in order to exit the cell, since packaging for membrane transport is much more complicated.
Unchecked, they would just exponentially destroy your tissue.
Cytokine storm responses are a particular kind of immune system over-reaction that can make relatively benign viruses much more dangerous to a healthy host then a more immunologically suppressed host, but that's not the behaviour of COVID-19 which is showing pretty standard lethality profiles.
No that's why I said there is no pressure to be severe. Killing hosts doesn't provide many benefits (unless you spread via people touching dead bodies such as Ebola).
