So a middle-salary employee is looking at a 25% increase in healthcare costs due to paying with after-tax money.
You can. It's probably not in your best interest, because the individual market plans are more expensive, but there's nothing stopping you.
> I know my company pays at least as much as I do for my insurance, but if I go off the company plan I can't get that money to use for insurance I like.
That's your employer's choice. They could provide a cafeteria plan, which would give you the choice (but again, since individual plans are always going to be more expensive for the same level of coverage[0], they'd have to pay more money overall to provide the same tier of benefits).
[0] simply due to basic actuarial math
You can always venture away from your employer and visit healthcare.gov or a relevant state exchange.
From what you're describing I think what you're looking for is an HMO - either a branded facility like Kaiser or a "provider network" that agreed to guarantee prices to that specific insurance company.
You won't gain much transparency though - every provider works off the master price list, and the insurance company then negotiates a discount highly correlated with the size of that insurance company and general presence in the region.
If I could buy health insurance separately from my company I'd look into it. I know my company pays at least as much as I do for my insurance, but if I go off the company plan I can't get that money to use for insurance I like.
The result of this is I have incentive to not care what anyone charges. The only thing I can do is lower my satisfaction job rating if the doctor I want to go to isn't covered by my plan. If I actually could choose insurance I would would look into cheaper plans - if they tell me the doctor I want is more expensive so I need a more expensive plan to cover using him I would then have incentive to choose: see if I like a cheaper doctor, or pay more for the one I like.
The result of employer providing my health insurance is a large source of dysfunction in the health care market. I illustrated one, but there are others. (Note, there are other dysfunctions in the health care market - always it is complex)