Discussions about NAT very often forget that it works by messing up with the transport layer. The fuzz is about hiding IP address and exposing services, but the worst thing about NAT is that technically it should not count as a connection to "the Internet". It exploits TCP/UDP properties to fake endpoints into thinking they have a proper connection.

To visualize this, imagine we somehow are out of available email addresses. Email providers have an idea, they would make one inbox for multiple people and have an SMTP proxy that will read the message content, look at "Dear ..." heading and proxy content as new message to "internal" network. All clients would see the same internal addresses from private space (picture 192.168.1.1), but upon sending the provider proxy replaces it adding "King regards, <shared address>". What if someone format the text differently? What if they use new format unknown to the proxy? It just won't work: https://en.wikipedia.org/wiki/Protocol_ossification Someone would then argue it is good as it hides your real address from spam and theft, but we can clearly see the massive disadvantages in this design.