Some older houses in the US still have the in-door mail slot. But for some reason, the Post Office doesn't seem to want to use them. My uncle has a perfect good mail slot in his front door and got his mail through it for decades, but recently had to put a mail box on his house. There's a mail slot in my front door and I'd be happy to get mail there, but the Post Office wants a mail box out by the street.
In older neighborhoods, the mail carrier walks from house to house and puts the mail in a mailbox that is attached to the house, usually near the front door. While people could steal from those, you had to walk up to the front door to do so, and neighbors could see you. That might have been something of a deterrent.
The Post Office is moving more and more towards having the mail carriers deliver the mail while driving. The mail boxes out at the end of the driveway by the street work well for this. In some neighborhoods and apartment complexes, all the mailboxes are placed out at the entrance to the neighborhood/complex, like this: http://www.sepco-solarlighting.com/blog/bid/107915/Subdivision-Mailbox-Solar-Lighting-to-Show-Green-Initiative
The mail carrier can drive up and deliver the mail without getting out of the truck.
There used to be a problem with thieves targeting the mail the day Social Security checks were delivered, but now that is all done by direct deposit.
While it might be sad that a birthday card or letter got stolen, there's no huge loss. The main thing that would be stolen these days is packages, and those could be delivered by the Post Office, UPS or Fedex. The latter two are not allowed to use mail boxes.