It's really not the small to medium, non-recurring bills that are priority worries. It's the big and recurring bills. In other words, "Ooops!" shouldn't be the worry; "Oh s**t!" could be.
The concern here, I think, is extended and extensive dependence, no matter what the cause(s). It could be a serious accident, or a serious illness, or whatever, involving major, long running care expenses, such as ongoing speech therapy, ongoing treatment for serious learning disabilities, long-term care involving assistance with the basic functions of living (bathing, dressing, etc.), expensive medications for chronic lifetime conditions, and so forth.
I don't have a terrific answer how to insure well against these possibilities given what's available. I suppose some combination of PA, CI, and TPD insurance (with a TPD payout, if it occurs, "bridging" to CareShield Life benefits) could help to a degree, but it's not a very satisfactory answer.

Having more wealth obviously helps, but "If I only I were more like Bill Gates starting today" isn't really an operable plan.
Does anybody have any other ideas?