No, they tend to become more spreadable, but there's no reason they couldn't become even more harmful as they evolve, rather than less. The strains that will win out are those that do less immediate harm (thus become more spreadable as people don't stay in bed ill), but that doesn't mean after a week or two they couldn't get really harmful (we saw in the first wave that covid was generally a week of nothing, a week of symptoms at home, a week in hospital, a week in intensive care, and then into the grave, with a certain chance of recovering each week. Imagine a mutation which reduced that recovering chance, that would cause more death, but not affect the spreading in the first week)