You can insure for almost everything, but the simple things you insure for with homeowners insurance are more food for the insurance racket than anything, because all those incidental costs are, like the superposter said, better covered with rainy day funds because you will experience several in your lifetime. In that case, better to manage your own money than give it to someone else just to give back to you after taking a cut. You would never have day to day homeowners insurance and not get catastrophic coverage, but you would certainly (and probably should, unless all insurance providers available to you are racketeering on the small stuff for profit) consider the reverse.
Except, believe it or not, that is what people want and expect now from a homeowners policy.
Simple Fire (HO-0) or slightly broader coverage (HO-1) essentially don't exist anymore for individual homeowners. HO-2 (Where the company says "We insure you for the following (long list) of things).") is also somewhat unusual now. People don't buy them unless they are very price sensitive.
The most common type sold is HO-3, where the the carrier says "We insure basically everything, with the following exclusions (like earthquake and flood)."
(Actual policies are much more complex, but that's the basic idea.)
And in fact, you do get the best of both worlds, because any carrier allows you to choose a high deductible, like $5,000 or more. So you can self insure the small stuff, (which the carrier doesn't want to deal with anyway, because of the overhead of settling a loss) and feel comfortable if say a pipe breaks during the winter while you are on vacation and causes $20k of damage, you are not going to have to come up with that money somehow.
