NAT (Network Address Translation) is the most notable legacy of a very different time: when the Internet was not widely adopted, and dinosaurs were roaming free. At that time, like... 20 year ago?, there was plenty of available Internet Addresses (was normal to be assigned a class C network with 254 public Internet routable addresses. I personally got two class-C, for iol.it and for matrice.it) and no one had any idea the ipv4 address pool will ever be exhausted. So, most machines on the Internet were there with their own public address. Also, no problems with security, encryption, and all that. There was no money on the Internet, so no crime.
Telecommunication was a matter of having the best way to connect two public hosts peer-to-peer. SIP was designed with that in mind, at beginning. So, it was completely out of its natural environment when in few years most of the hosts using VoIP would find themselves behind a firewall and a NAT. Different IP addresses if you...