My insurance, which I am now paying for on COBRA (made affordable by a 65% subsidy in the stimulus package, thank you!) does not cover annual physicals!
Seriously, the one thing that could help reduce the severity of chronic diseases is early diagnosis and treatment. The other thing is regular monitoring. But my insurance, like many others, does not cover this. It only covers mammograms after age 40, although it covers annual pap smears before then.
It does not cover routine physicals for men, in spite of the fact that many male problems like prostate cancer and heart disease benefit from early diagnosis and treatment. It only sort of covers the reproductive system for women, but not general physicals. Yet thyroid, heart disease and all of those problems are best treatable when diagnosed early.
IMO, any health plan, public or private, should be required by law to cover general annual physicals for adults, just like many cover well baby and child physicals. The long term cost savings, not only in terms of cash but misery, would be staggering.