Earlier quoted context omitted.
Preventative care is free because it saves a tremendous amount of money for the insurance company and physical and emotional hardship for yourself by catching bad things early.
Your view is a commonly-held one, and makes a lot of sense; unfortunately there is very little support for it. One data point to the contrary is the Oregon Health Care Study, which showed that 'free' preventative care increased healthcare spending, but did not improve lifespan or reduce long-term cost.
So hey, at least in my case, it worked as the commonly held belief states.
And that study doesn't look at multi-decade long term effects like diabetes, etc. where you need it for a decade (or longer!) untreated (or poorly managed) before it kills ya. But it still kills ya years early.
So even the "raising rates of diabetes detection" in combination with your belief from that study proves you incorrect when people talk long term.