Generally speaking. I (rarely) buy insurance for things like travel when I have reason to think that I have circumstances that may lead to a higher probability of collecting insurance than the average person automatically buying it has. And I certainly have things like homeowner's insurance where losses could be catastrophic.
But self-insuring for random relatively low-cost events mostly makes little sense for people as it does for companies.
Many types of insurance that protect payouts to third parties include provisions that the insurer handles the lawsuit to defend the claim. This can be a convenience even to a wealthy person, especially one who doesn't get sued much.
Insurance companies are always going to give you unfavorable odds, unless you think for some reason youre more likely than average to have an accident.
I don't understand why car/home insurance isnt nationalized
Reducing variance in a random outcome still has value. For instance, you might have the money to cover an adverse outcome, but if you could guarantee you wouldn't need the money, then you could park it in an illiquid asset (e.g. some type of investment).
Insurance for your phone, computer etc for example is certainly stupid for most people.