This thread is a total math failure. Surprising given the number of smart individuals on this site.
Assuming insurance companies do math and statistics correctly (which is their job), you always pay a premium for insurance over the risk times the estimated damage from a claim. That's why you don't get insurance for things you can afford to lose.
We all get that when we refuse the extended warranty at Best Buy for the $100 gadget (or whatever the current example of such things is). Best Buy pushes it because they make money off each warranty because they've priced the risk correctly, and you understand that and know that you can afford to lose the $100 item and so refuse the warranty.
The exact same analysis applies to a house. If you are truly indifferent to the loss, then you should not pay a premium to insure against it. MMM is likely safe on two fronts: (1) he can afford a total loss of $400k (really probably only $200k replacement costs) without any impact on his finances, and (2) he knows how to build things, which reduces his out-of-pocket expense if disaster strikes.
But the idea that it's just a few bucks to insure, so of course do it is a logical fallacy. Assuming the insurance companies priced the risk correctly, those few dollars are more than (1) the likelihood of claim times (2) the amount of claim.
There is only one exception to this rule that I can think of: the cost of repair/replacement. If the insurance company can pay less than you for the repairs (e.g., because Geico owns the auto repair facility and therefore pays the hourly wages of the workers rather than the hourly fee you pay for service), that might increase the odds in your favor. You see this with medical insurance where the doctor's "fee" is $200 but the doctor agrees to take $50 from Blue Cross. But that should be the only factor in play other than whether you can afford to bear the loss.
There was a similar thread on life insurance a while back, btw, and the same results apply. Insurance companies are better than you at statistics, so life insurance will statistically always be a loser. You get life insurance if there are things that you have to provide for and cannot if you die. Once you get past that point (i.e., have enough assets to cover those who depend on you), there is no reason to have life insurance. It's just math.