It’s priced that way because Medicare has to get the best price by law. Everyone else gets a lessor discount, with cash payers getting nothing by default.
It makes sense - the largest payer should get the best price. But it doesn’t make sense because it’s not really a market.
We’d have much better outcomes with a Medicare for all model, and then private insurance could actually be priced with an insurance model and be used as a fringe benefit again.