Having perfect knowledge of the cost would be doubly scary, even at half the current cost. Many co-pays for basic procedures are fairly small, less than someone would spend in on an impulse buy at the department store, so you have no basis to extrapolate that knowing the full, exact amount would somehow induce greater compliance, when compliance with much lower bugetable amounts is resisted.
A real world example: in the 60's Congress acted on the information that only about 50% of the population went to see a dentist routinely. They funded dental schools and helped push out a ton of dentists to serve the unserved. Forty years later, there still is only a 50% compliance rate. That suggests that the problem is not in the supply, but the demand. There are many well-known irrational factors in the human psyche that invalidate your hypothesis, not to mention the rational ones I have presented.
More significantly, not all serious disease is preventable. People can lower their risk, but not eliminate it. Treatment of many serious diseases is completely unaffordable already by the majority of the population. There is zero chance most could ever budget for such contingencies, ever.
*although if people have no choice, and if they can afford to travel overseas, sometimes take on additional medical risk and go abroad to get essential medical treatment. It's called medical tourism. That is not an ideal medical solution however, since the hidden cost is the risk inherent in travelling when ill and possible post-op complications which would necessitate expensive retreatment at home anyway, possibly then bankrupting the person.