If you find an object with no obvious owner, you either leave it where it lies, or you report it by turning it in somewhere. To the business where you found it, or the Lost & Found department of the transit authority, or the police if all else fails.

I don't see anyone calling up the police to say, "Hi, I found <item> and I'll keep it until someone comes over here to claim it!" because the only people coming over will be the police themselves.

Every place with a Lost & Found service, and the police, regularly liquidate the unclaimed property. You can find lists and auctions on your civic website if they're selling the stuff. They may also donate it to charity or destroy it.

The police or anyone else are not going to stick a tag on a box with your name and number so you can come to claim it after the grace period elapses. That's not how claiming stuff works.

If a package falls off a truck in front of your house you can pick it up and inform the authorities, who'll in turn inform the owner.

If the police or owner care enough to pick it up they can have it, but presumably there's cases where they can't be bothered, then it becomes abandoned property and you can keep it.

Just because you find abandoned property you don't need to go out of your way to mail it to the owner, just inform them and they can come to you.

The "why not just leave it?" aspect of this is easily defended, if the package e.g. contains electronics they'd be damaged by exposure to the elements.

This of course varies a lot by jurisdiction, but yes, in many places that is exactly what the police will do.