[nabilhat]

Police actually often do retrieve stolen bikes! Not most of the time, and not because stealing a bike is a crime, and not because they know it's stolen. In the US, if one or more bikes are in the posession of the (ahem) kind of person that your local police have motivation to shake down, they may be confiscated if they're in that person's possession when they do.

If the bike is valuable enough to be worth the effort, it will eventually be listed for sale by the police, usually through an "unclaimed property" continuous auction system. If the bike doesn't clear whatever value/revenue threshold that is, it'll be scrapped or donated and that's that, or sometimes it'll end up bundled with a bunch of other low value things as a single auction item.

If your bike is valuable enough to generate revenue greater than the expense of auction logitics and is stolen in the US, pay attention to police auctions in your general area and it's likely to turn up. Sometimes they'll skip the sale and give it to you if you have documentation proving that it's yours, sometimes they want you to point them to the police report you filed saying it was stolen. Sometimes they'll lol and you have to pay up anyway.