If the insurance was worth $229/month why wouldn't our 29 year old purchase health insurance? Why does he have to pay $52/month tax if he doesn't?
I see you are making a common mistake here. While the insurance has a price of $229/month to our hypothetical 29 yer old, what it is
worth to him could be more or less than its price. If it's worth more to him than it's price he'll buy (unless he can find other things that are worth even more to him at that price that he could obtain) If it's not worth $229/month to him he won't buy. It's elementary microeconomics, which far too many people tend to ignore, including many who should know better.
Also since the $52/month is a sunk cost for him in this scenario, the actual cost of his decision to but insurance is not $52/month but $177/month ($229-$52). Hence the purpose of the tax is to make the cost of insurance lower, altho the price remains the same.