The insurance companies want to see appliances tested and certified by agencies here in the US following our requirements and guidelines. I can't blame them. I suspect a non-UL appliance would raise an issue with the insurance folks, but why don't youy just ask your agent?

I have had insurance policies (and claims) with several insurance companies, none of which ever asked to see if there was a UL logo on anything. They took a few pictures of the outside of my home, and then took my $$$. Of course, YMMV...

That's a stretch, most people don't even know what a UL listing is. Do you think if you unknowingly (or even knowingly) bought a non listed extension cord (yes they do show up here)your insurance would be void? Your insurance company is bound by law to cover you unless they ststed it in the policy beforehand, even then a good lawyer could probably get around that.

Think about this, if you cause an accident while driving drunk, your insurance must cover you. They can cancel your coverage after the incident, but they are still bound by law to cover your damages.

Of course with all the exclusions in homeowners insurance lately is would be wise to read your policy carefully, along with any additional exclusions added after the purchase. The insurance companies all cried broke after all the hurricanes and began to exclude coverages and raise premiums, now the financial news reports record profits for them.

What strict European standards are we talking about? Most European equipment that I'm familiar with is self-certified by the manufacturer and not a dis-interested 3rd party.

I think Joefixit2 has it covered, check your policy. Not only is there some equipment that is not listed (BTW, UL is not the only listing agency in this country, just the most famous), there is a bunch of equipment that bears counterfeit labels and it is usually Chinese.

I have never had a claim investigated or denied in the 30-plus years I have had Allstate homeowner's insurance. Granted, I have only turned in 3 or 4 claims, but one of them was a real doozy. The hot water supply hose to the washing machine broke while we were out of town and ruined the entire 1st floor wood parquet flooring, the baseboards, some of the furniture, and the lower 1/4 of the drywall. We decided to replace the parquet with high quality carpeting and Allstate's agent agreed to pay for everything we asked for without even coming out to the house to check on the extent of the damage. I found out later that the carpet cost
Allstate less than replacing the oak parguet flooring would have cost, so maybe that's why they agreed on the carpet so easily. I wouldn't worry about buying a UK appliance unless Allstate has recently changes it's claim settlement procedure, but you might want to check with your own insurance agency before you install the cooktop just to be sure.

Read your policy.
If you have the typical 'all peril' type it covers everything NOT excluded, including your own mistakes.

The investigation after a fire is to try and find someone with deep pockets (or insurance) that the fire can be hung on.
An electrician that used incorrect parts, a plumber who installed a gas line incorrectly, etc.
You are insured against any work you have performed.