I'm not (yet) willing to do this for general health insurance, but I made this decision for dental, a couple of years ago. It has not been an issue. I've had a couple of crowns, and paid a fraction of what insurance would have covered, minus the ridiculously high deductible, and the monthly premiums.

Of course, now it's time to re-up for next year, and the message seems to be "Squeal, boy!".