Insurance is worthless until you need it.
Exactly.
Statistically you are likely better off without it. This is a simple conclusion since if the insurers were not making money off the insurance, they would not offer it.
Which is only relevant if you happen to have a reset button on your life you can press multiple times ;) The assumption that just because someone makes money off something that it isn't in your interest to purchase it is not sound. Pooling and diversifying risk costs money. Now, whether you are being charged a fair price is another question...
But like another person said, if you can't self insure the entire thing yourself... well buyer beware.
Yep. The standard advice here is self insure up to the level you can and then buy insurance for catastrophes. Catastrophic insurance (high deductible) is inexpensive and is also the range in which insurance companies are actually bringing value to the table (by pooling risk). Low deductible insurance begins to blend into a service plan which is both expensive and of no real value to the consumer while high profit to the insurance company.
As others pointed out you certainly don't want to pay for insurance you don't need (i.e. parts the HOA covers) so make sure your insurer proper aligns your coverage.
You will find that even savvy investors can be surprisingly irrational and dumb when it comes to insurance. Most people simultaneously over insure some risks and drastically under insure other risks. Insurance deals with fear and so it is a natural part of personal finance to get irrational. It is silly to build up a stash with sound investments but be penny foolish when insuring against outsized risks (e.g. liability, disability). And it is also silly to pay to insure things that don't need it (e.g. extended warranties).