Wow, that sucks.
My insurance covers what they call preventative visits, which include annual physical and blood work.
But somehow there's always some test during the physical that isn't covered, and they stopped giving me the cough test, that was half the fun. I have an HSA, so I pay 100% for the first $4000, before co-insurance kicks in.
I went to a rheumatologist last year, $500 for additional blood work, 5-minute talk and a guess at some medicine. If it didn't work, I could come back and let her guess again. No thanks.
I'm actually very happy with my health insurance now. I'm also happy that my daughters are doing well, and I haven't hit my max out of pocket in a few years.