It really wasn't my intention for to get into this... but...
I agree completely that keeping up w/ your health is super important, and routine monitoring is a great idea. It's fantastic that insurance companies will provide physicals at no cost, or even lower premiums if you do. Thats a model that all should follow, it saves everybody money.
That's why I said, mixed feelings on spending EXTRA money on it. If it's free, by all means do it!
The problem is, your typical "physical exam", by the somewhat limited, defined version of what is included, is a pretty limited assessment of your health and and the potential for "finding problems" that you don't already have a suspicion about. That is, the technical examination part is kind of like taking a car to mechanic and saying, "Any problems w/ this car? But you can't turn it on or off, or open the hood, or drive it around." Most of things that would be found during the physical exam, you'd have some kind of discomfort and know about already.
Really the important part of the exam is just the time talking to the doctor, the info he gets from YOU, and vice versa, in talking about any problems you may be having, how you're feeling, etc. If you have a doc that has the time for a real chat, and really pay attention, this can be invaluable and worth your time. Unfortunately these days that is rare.
But you can get the same thing by having a buddy or two that are doctors and having a beer w/ them every now and again.
Now once again that's assuming that you're willing to go to the Doc on your own when something seems off, and proactively monitoring your own health.
I know a lot of people (guys) that are like, "I have this funky pain in my abdomen when I lean to the left. Go to the doc? Nah, I have a physical exam in a few months [meaning 6...] I'll just talk to the doc then".