I don't totally disagree with your broader point, but there's a decent case to be made that basic preventative care reduces costs by catching issues before they become expensive, chronic conditions (or worse.) The 'preventative care' that is 'free' is usually pretty basic: yearly physical, scheduled vaccines, and basic blood tests and cancer screenings at certain ages.

I'd also question what health insurance plans still encourage 'using as much as possible'. Most are high-deductible plans, where you are paying $100-$150 for an office visit until you hit your deductible or OOP max. The days of $20 copay doctor visits are gone for most of us, unless you are on Congress' health plan.