At my native home my bicycles are insured, now through my home insurance (part of the furniture, kind of), but at one point one of my electric bicycles was too expensive for that and required additional insurance. As soon as the price dropped a bit I could drop that extra insurance.

As the comment above said, in Japan a bicycle is registered to a person when you buy it. Even the second hand bikes from recycle shops. And there _is_ a theft problem.. but not everywhere. I sometimes don't bother with locking my bicycle outside the shopping mall, here (in my town in Japan). Nobody steals bicycles here. There was a time when a particular gang of teenagers would steal scooters though.. the 50cc ones. A friend's scooter was stolen. The police found the culprits and he got his scooter back. But not much problems with bicycles. Unlike in my town back home. Now that I'm here I would not be surprised if, when I go back, I find that someone broke into my garage and stole the bicycles.

It's not insuring the bike itself, it's insuring damages for accidents while riding it.

If you run into someone on your bike, you're on the hook for their medical costs (yes even in Japan's universal health care system, it's not single-payer), loss of income, etc.

Insurance will pay for that. It's now legally required to hold bicycle insurance in most cities in Japan when riding for this reason, similar to requiring basic car insurance.

They are easy to steal and can cost multiple thousands of dollars.