Huh, I had to ask specifically for it during my annual. Still salty about that since my insurance supposedly covers annual physicals but asking for the test meant that I was going beyond a routine physical and so they coded it as an office visit and billed me a not insignificant amount for it (for the visit, not the test itself, which was extra). Talking to the billing department and the insurance company got me nowhere.
I donate blood. The American Red Cross sometimes gives away small gifts ($5 Amazon Gift Card, windbreaker with ARC logo, etc.) to promote donation. The are now testing blood for COVID so I've had one free negative test so far.
There are different tests that you can get from places like LabCorp or Quest Diagnostics - doctors working for these places prescribe the test. Anyway, since ARC is testing your blood anyway, it seemed like a reasonable incentive would be to test your blood for Vitamin D deficiency. Or testosterone or cholesterol levels or whatever you wanted from a menu of choices.
That would be nice but blood tests aren't free and blood banks would have to pass that cost on to their customers. The main reason they tested for SARS-CoV-2 antibodies was to identify potential convalescent serum donors.