In order to self-insure, you need to be uber wealthy. Having $2M in retirement, for example, won't cut it. A relative of mine is in a nursing home right now after suffering a stroke. She is paying over $7K per month for that luxury.
In addition, she gets bills for things that aren't covered under the standard nursing home care. For example, she developed an infection in her foot and she needed some kind of boot or something and some medication. That isn't part of the care. It would come under her insurance policy. She, however, did not have a prescription plan because she was perfectly healthy (or so she thought) before her stroke and took minimal medication. For the last few months her "extra" medications and such for some infections have come to $2500 per month!
Fortunately, she did have LTC insurance, which is paying about $5K of her nursing home bill. But everything else has been out of pocket. If she didn't have LTC, she would have blown through her assets pretty quickly.