"First of all, "mandatory insurance" is an oxymoron.  Secondly, the pricing for something mandatory" necessarily means prices will skyrocket (see everyone with an Obamacare-market policy).  This has led to double-digit percentage increases for absolutely everyone.
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Instead-- why don't you pay into your own, PRIVATE account for catastrophic coverage, and privately buy your OWN policy, which you brokered directly with insurance provider?  By forcing government and employers out of the equation, we would single-handedly drive prices down for everyone.  No more deadweight loss, no more bloated government costs-- just you and your insurance provider. That's it.
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Additionally- a medical practice charges ONE amount for the same service. ONE.  You would be able to shop for the best price, and your insurance would cover a certain amount-up to and including the whole thing, again, based on ONE price.  You know-- sort of like EVERY other good or service on planet earth?