It's going to be impossible to avoid reinfection completely for the entire future.

But I have a suspicion that part of the reinfection issue is there is so much virus around that people are being exposed a lot and thus being reinfected very quickly...

To me, this just means to mask up indoors for a while longer. I have not had symptomatic COVID-19 despite a couple of confirmed exposures (one of which was when there were no tests to be had so I have no idea whether I got an asymptomatic or extremely mild infection or not).

The other issue with the study, although I'm not saying we should let down our guard, is it didn't really correct for the possibility that people with underlying conditions may in fact be more vulnerable to reinfection because of a weaker immune system that did not mount as strong a response. The study authors admitted this might be a factor. In other words, people who have been infected and have underlying conditions may want to be MORE careful for the three months after the infection rather than LESS to avoid a rapid reinfection.