Hahaha that's a good one... especially as we're talking about Miele here. ;-)
And you're factually wrong anyway.
I didn't say "home insurance", I said "household appliance insurance". Different thing, unless your home insurance happens to cover appliances.
My household appliances insurance is not expensive. It covers 5 appliances, unlimited call-outs, and you don't get screwed at renewal time if you've claimed on the insurance.
As I said, I've had Miele out A LOT over the years and I've never paid them a penny, and trust me on some of my older large appliances they've pretty much replaced 100% of the internal parts.
Either way, the insurance company will turn a profit from premiums. I'm glad this policy has paid off for you, but "reducing costs" is not a good reason to purchase insurance. Insurance reduces risk and makes expenses more predictable.
Put the two together - insurance and appliance servicing company = your described scenario.
e.g. I have a Samsung 970 EVO Plus SSD drive that has just failed, and lost some of my important data. Its got a 5 year warranty and is only a year old. I doubt I will bother to go through the warranty claims hassle, because the end result is not worth it.
I would have to send it back to Samsung, with my commercially important data on it locked in the chips, and get back another drive which it seems is not particularly trustworthy to rely on again. I've had 2/5 Samsung SSD drives fail and won't be using them for anything important again, I've just ordered a Hynix to replace it.
Another case, I have had a washing machine fail under warranty recently, again about 1 year into a 5 year warranty. It took 7 weeks and many frustrating phone calls before someone came around to actually fix it. Next time I won't bother to get a new washing machine, I will get a second hand one, and when it breaks I will get another second hand one immediately so I don't have the problem of not having a washing machine for sooo long.
My sister in law's oven failed with the self cleaning lock activated. It's an in-wall unit so the repair tech could only think to start cutting apart the wall. Instead, I took a hacksaw blade and painstakingly sawed off the lock. Since I was already committed, we then pulled out the unit and bypassed the failed thermal switch long enough to "unlock" the mechanism. That probably saved at least $1200...
If the goal is convenience, then definitely. Home insurance policies are quite a lot more expensive than actual repair costs are likely to be. Which of course is expected, the product being sold is peace of mind and convenience -- both of which people happily pay a premium for.