Well, first of all, I'm not doing any self-testing, because there are no home testing kits to be had at the moment in my area. A lot of people are getting tested due to known exposures (day care, etc.)
But if I do become symptomatic, I want to know if I am positive and therefore contagious, so that I don't spread it to my family, to my church, peeps in the grocery store, etc. It's to protect others.
Edit: here follows the tl;dr. My primary reason is ^^^^^.
Also, even though what I've read is that immunity acquired via infection is not as strong/ long-lasting as immunity via vaccination (begging that we don't all start arguing on this), if I knew that I had a proven case of Covid, I could use that date of infection as a "shouldn't need a booster until X months later", or whatever the guidance is at that point. So for instance, first vacc Jan 25 2021, second vacc Feb 15 2021, booster Oct 1 2021 (8 months later.) If (spitballing the number here) research shows that the booster effectiveness wears off 6 months later, and they recommend another booster (would be April 2022), but I had test-proven Covid in March 2022, I might postpone another booster for X months. If this happened, it would be entertaining to spring this on my poor doc to let him figure it out.
In the end, I'd go with the published guidance. Since we just don't have decent data and easy testing for cellular immunity (the kind that keeps you out of the hospital), I doubt that trying to fine-tune individual cases is very helpful.