Only once since ... 2015? About 10 bikes or frames, total. And that includes some pretty premium-priced frames and two complete bicycles (non electric), one from a manufacturer (Guerilla Gravity in Colorado) and another from a local bike shop in New England selling a very pricey bike (Surly Big Fat Dummy) over the internet. I have had to crawl around and find the SN on every frame I have reported to my insurance company.
With that said, the GG bike was a fully custom order, so the receipt I had for it would have been easily verifiable. Same frankly for all the other receipts I had, and I got one for every purchase. The serial number would be nice but not a requirement for verification with the police if a dispute arose. Maybe your insurance company would feel different but mine settled for just a picture of the bottom bracket with the SN on it, coupled to the receipt.