Don't know about there in the States, but here in Germany, getting a positive test result - while initially an inconvenience (what with the mandatory quarantining and all) - did bestow, upon subsequent recovery, the (unvaxxed) individual enhanced rights, comparable to those of a vaxxed person, at least for three (or six) months.
Of course, in the case of this person, who had been repeatedly vaxxed anyway, I don't see any sense in this.
Regards,
The only thing testing positive for Covid does for the unvaxxed in the U.S. is to give us a reason to say why we are not getting the jab. It is recommended to wait three months to get another jab after one tests positive.
So I make sure to test positive every three months, whether I actually take a test or not.