Doing that could also drive up the price of oil changes such that they're no longer affordable without the use of insurance. If you could get an oil change for $50, then most people could afford it by paying for it outright. If that oil change now costs $500, then most people would have to go through insurance, and get the "discounted" price of $100 (which either has to be paid if the deductible has not been met, or you end up paying 10 to 30% of it).
It also catches things that require long expensive treatment early enough for them to be treated, rather than treatment be pointless, and, even if attempted, of shorter duration (on average) than if the conditions were found earlier, which is why preventive care doesn't seem to reduce aggregate costs.
The best way to reduce aggregate healthcare costs, if you have no other priorities, is to just make people less likely to seek care. No care = no costs.
Goods and services are allocated by price or by time. Take out the price component and assume that people will go to doctor more often, obtaining an appointment will take longer. How do time and hassle required to see a doctor disincentivize well visits?
More importantly it leads to less people dying of preventable matters. What you seem to be implying is that its a net negative to which I say citation needed.