They're not the same as the classic US mailbox ().
In the US you can use such a mailbox to send mail as well. In Europe you typically have private letterboxes for incoming mail and big, public post boxes for sending.
Missing link? In NZ, and presumably other countries, personal letterboxes in rural areas can be used to send too, which I'm guessing is the same as what you're referring to.
Yes NZ is one of the four countries that use this style of full duplex mailbox. It hasn't caught on outside US/CA/AU/NZ, probably because (speculating here) it's not secure against theft and doubles the workload for the mailman.
They do, they just look different. At least that's how it is in France.