Though note that an insurance may regardless be useful if you have self-control problems with regard to money. If you've paid your yearly insurance payment, the money is spent and will protect you for the rest of the year. If you instead put the money in a rainy day fund, there may be a constant temptation to dip into that fund even for things that aren't actual emergencies.

Of course, that money being permanently spent and not being available for other purposes does have its downsides, too.