There's some nuance here: It might be that a rational insurance provider encourages their clients to do regular checkups for conditions that can be caught early and treated at a much lower cost.I'm a member of Kaiser HMO, and they do just that -- they regularly notify me of screening tests I should be doing and they offer several ways to contact my doctor without actually seeing my doctor.
If I'm not sure I need to go in to see him for that lump on my toe, I can call a triage nurse for advice, set up a phone call appointment with my doctor, or do a video chat with him.
For my last annual checkup, my doctor emailed me, asked me to go in for some bloodwork, then a few days later, I went to visit the doctor and we talked over the results while he conducted the physical.
I know some people don't like Kaiser, but I've had only good experiences with the system, and I love their electronic records system - I can view test results online, and if I'm referred to another doctor, the other doctor has instant access to my records.