If you don't have cash savings as a homeowner, you can leverage a home equity loan or line of credit to cover those emergency bills. In times of extreme low interest rates, it may even be beneficial to do that vs. paying with cash.

If your household is a typical HN high earner, and you are early in your mortgage's amortization schedule, the tax money you save by deducting interest can fund a $10k emergency repair fund too. Maybe even in less than a year.