There was a time -- before the rise of NAT -- when one could directly establish connections to others across the Internet without having to jump through hoops or implement other tools (port forwarding, UPNP, a third-party(!), etc.) to do it.
In general, as a network engineer, I dislike anything (especially NAT) that breaks end-to-end connectivity, simply because of the inherent problems that arise as a result.
In addition, some of the DDoS attacks we've seen recently would be a lot easier to prevent if NAT wasn't a thing (e.g., as an ISP, I could easily shut off a specific device; I can't just shut off a customer's entire access).