There are (or at least were when I sold insurance) products that costed very little (compared to an actual plan) that provided you with the negotiated price the insurance company would pay if something happens. If you can afford to self-insure, the best bet would be to buy one of these products and store the rest in the bank.
No clue if those things exist anymore with everything going on in the world of health insurance, though.
But you really can't afford to self-insure, even if you're young and healthy. There's always the small but real chance of getting a catastrophic illness and running up a million dollar bill.
Therefore, you really need to buy at least catastrophic coverage. And that's real insurance, not self-insurance.
Health insurance is complicated because for most people, it's so much more than just insurance. It's prepaying $300 a month so you don't have to pay $200 to visit the doctor once per year. No, I don't know why people do that. You're right that paying $100 a month for "please reattach my severed limbs" insurance is more affordable. Terminology be damned, that's possibly what people mean by "self-insured". They pay day to day expenses out of pocket.
No clue if those things exist anymore with everything going on in the world of health insurance, though.