Are you sure about that? The CDC suggests many similar complications (which would cost exactly the same to treat regardless of the genesis of them) according to their website and indicates [mostly un-vaccinated] people die from chickenpox too. The comparison surprised me too, but seems to be remarkably appropriate.
The study published about a month ago found more consistent protection, i.e., the mRNA vaccines produce a consistent level of spike proteins and therefore antibodies in all recipients, whereas some people who had milder prior COVID infections did not produce the same level of antibody response.
The unanswered question is how much that's protective against future infection. Nobody really knows. Antibodies are an important part of the immune system, but the real key for long-term protection is the effect on memory T-cells. I'm not aware of any studies on that topic.