The Onion

That's called self insurance, and it works if you can afford it. The thing about insurance is that it is fundamentally a negative expected value financial product. That negative EV is the premium you pay for the reduced risk. And the risk reduction happens immediately, instead of needing to wait a decade for your self insurance fund to build up.

One way to see this is to look at what the people who most understand insurance do. Insurance companies have a problem if too many people make claims at once. They could self insure against this risk, but that takes a lot of capital that they do not want to spend. Instead, insurance companies go out and buy insurance to cover them in case something happens that results in a lot of claims (this is called reinsurance).

You can actually pull a similar truck with your own insurance. Self insure for the amount that you can handle, then treat your insurance provider like a reinsurance provider to cover large events beyond your capacity. In this case, we call it having a high deductible plan. And you can increase the deductible as your savings increase.

Of course, once you have enough capital to self insure the full value of a house, you need to ask if self insuring is the most profitable use of that capital. You could also pay a premium to insurance companies for the financial service of risk reduction, then invest what would be your self insurance fund in something that you expect to produce higher returns.

Of course, now you have the risk that this other investment might perform poorly and you want to insure against that. In this case, you might invest in something you expect to perform relatively poorly, but would do well in circumstances that makes your other investment do poorly. Of course, figuring this out is difficult, so you can instead pay a premium to an investment fund that specializes in hedging their bets.