Well, any insurance is a gamble - if you think about it, you pay in a lot of money and then benefit if you need to claim.
You then risk assess the consequences of not having insurance.
So, I hate to think what I've paid out in house insurance over the decades without any major claim BUT should I have a disaster that means my house were destroyed, I couldn't ever afford to replace my house without insurance, so I continue to pay it.
Car insurance the same (plus, with car, of course, it is the law)
OTOH, boiler contracts, in my experience cost a lot more to pay out for than you are ever likely to need to claim back. You'd probably find, when reading the small print, that major work would be excluded from their cover anyway, but do the maths of paying out £20 (or whatever it costs now per month) for years, against what you actually pay out for repairs. Last couple of times I've called someone out, I paid £100 and £80. That was over a space of about 4 years. SO I've spent £180 over 4 years on repairs and £280 (£70 per year) on an annual service rather than over £900 in monthly fees. Obviously there is a chance that you will suddenly need to claim before you've built any savings, but, would putting £100 is on a credit card break you ?
It is all about risk assessment. If you didn't have cover, and needed to call out someone, could you 'borrow' that from somewhere if you didn't have enough saved (be that a savings pot, a credit card, an over draft, or somewhere else). So, for a boiler repair, most people could, but for a house replacement, most people couldn't.