This is a good point, and I think it is reasonable to start with the immunity assumption, since it is generally the case for respiratory viruses.
Still, I wonder what the math looks like. It has indeed been shown that flu outbreaks in ideal conditions are more intense, but conversely, the flu seasons are shorter [0]. If medical attention makes a significant difference in patient outcome, then the longer virus season is presumably preferable. However, the significance of medical attention needs to somehow be weighed against the total number of people who end up being infected and the costs of shutting down pieces of the global economy for longer periods of time (not to mention limiting individual rights.)
Consider that less vulnerable people may be more likely to become infected in their daily lives since they are more active and likely come into contact with more people. In this case, a faster outbreak with many mild cases may actually result in faster herd immunity, and therefore fewer total infections in vulnerable populations. Perhaps a partial quarantine of at-risk populations is the best solution.
[0] https://www.citylab.com/environment/2018/10/big-cities-have-...