Not necessarily: I gain the ability to switch insurances (imagine, for example, a "free market" where insurance has to compete…), job losses or changes don't affect my insurance, etc. Actual competitive pressure and lower switching costs should, in theory, drive the price down.
Also, IIRC, insurance premiums paid with post-tax dollars are deductible, so they're not really post-tax. However, that deduction is part of the itemized deduction — while currently most people are not itemizing (as they do not have enough itemized deductions to hit the "it is worth it" threshold), my napkin math says that throwing HC premiums in there — since HC is so damn expensive — tips the scale / breaks the threshold for basically any normal income level.
But this is also an "imagine if" thread. Imagine if we made healthcare premiums outright deductible to alleviate the problem you've identified?
I also was buying out of pocket while employed for awhile. Unless you have a qualifying event you can only switch insurance at the beginning of the year, at least from the insurance options I was able to find that fit my family.
I honestly didn't even realize the thing about the standard deductible until I had already done it. I was shocked to find I couldn't deduct it because I'd have to use the itemized deduction which would have been lower. I just assumed my insurance could have been deducted like it was when I bought it through my employer... how wrong I was.
But yes I would absolutely prefer the "imagine if" scenario.
But you're right, this taxation intertwine is another tangle that shouldn't exist. Too much energy is spent by everyone trying to optimize take home pay, coverage etc.; and lower wage workers who just don't have the mental cycles to do any thinking get shafted.
It's not a compelling argument for society, but it's a compelling argument for the individual at the instantaneous moment of making that microeconomic decision.
If you accept higher wages to pay it for yourself, it's a bad deal, either to the employer or to you or possibly to both.