No one locks their bikes in Japan, either. According to Wikipedia this is thanks to "strong policing and general public disregard for stolen items." I can certainly say I've never heard of a US police department doing anything proactive in response to a reported bike theft.
In Japan every bike is officially registered and has a sticker with a number (think of it as a license number that has to be read closely). Foreigners are stopped by the police fairly often in Japan to check their bike licenses according to reports in /r/japanlife.
When I lived in Minneapolis, police encouraged a bike registry; they'd send you this serial number sticker plate that affixed to the frame rather well.
No doubt many flaws with that, I don't know if it helped. But I got a sticker.
(3M home town... they are good at sticking things together.)
People lock their bikes... just using the ring lock in general. If only because you need to put the key in to unlock the ring lock (and ride the bike) and then when you're somewhere if you don't lock it your key is just on the bike.
Of course it's a tiny ring lock. It's to stop unmotivated people and also people just taking the wrong bike. But works well enough.
Probably not 100% but "no one locks their bike" is incorrect.
You also have to to do some paperwork for buying a bike. I assume you have to transfer ownership when selling, so stolen bikes probably cannot really be sold on the open market.
Out of sheer ignorance: what are the implications of not having the proper paperwork? Do Japan's street policemen take note of suspicious looking bikes and follow up with their owners?
The police stop bicycles and ask who it's registered to. They can look up the registered owner from the registration sticker. If you stole the bike then you don't know the name of who it's registered to. In general there's no requirement to carry ID (apart from for foreign nationals) so police can't rely on cross checking against the ID people are carrying. Also, bicycles might be registered to a friend or a family member, so knowing the registered name and providing an explanation should be enough.
If you have no idea about who the bicycle is registered to then the police will likely make further investigations.
I have been stopped when driving suspiciously at night. I do not know what exactly constitutes suspicious, but the main thing they do is check whether your bike paperwork is in order, and (as a foreigner) that your residence card is valid.
in japan bikes are stolen once in a while by drunk salarymen who dont want to wamk to go back home. so not 100% safe but fairly safe. also all bikes have a registration number so you eventually find them.