For what it's worth, the Spanish flu actually mutated to become much more deadly than what it was at the beginning of the pandemic. It did go on to become less deadly after that though, in some part due to the more severe strains killing people faster than it could spread.
With the new coronavirus, there really isn't a driving force to cause the virus to become weaker in time. Incubation period is about 5 days, and for those who die, average time from symptoms to death is about 18 days. This means that people that have contracted a fatal case can still spend more than a week going about their daily activities, spreading the virus. With the Spanish flu, some people were dying the same day they showed their first symptoms, and this type of presentation limited spread. The coronavirus is a slow bake without a mechanism like this to favor weaker strains.
I don't expect this virus to start killing young people in numbers like the Spanish flu. I am concerned, however, about the potential long term effects of the virus (lung/heart/nerve damage) or even autoimmune issues. I'm fairly young, but I'm avoiding this virus like the plague.