Do annual checkups involve blood tests where you are? I've only had blood taken as part of one once, and that was in direct response to a new diagnosis of a health condition in a grandparent.
Of course, blood and urine. I do them every six months, even though my insurance only covers once a year, I'm happy to pay out of pocket for the second.
Mine do, yes. Kaiser in Northern California region.
I think the optimal move might be regular (possibly more than annual) blood work and only talking to a doctor when there's symptoms.
And if the results look dramatic, get a second or third opinion (and check) before doing anything.