I thought with more mutations, viruses become less deadly and stop killing their hosts (if it does so, the virus dies too)
This doesn't apply to covid, or any other virus which is transmissible before the onset of symptoms. It doesn't care how ill or dead it makes a host from which it has already moved on.
If it as mild as is being reported, Omicron could be a great natural way to improve the population's immunity
We do not yet know how mild it is. Nor what sort of abilities the next variant might have to evade immunity. There might be no evolutionary imperative to change how ill it makes the hist, but there is an enormous one favouring vaccine-escape