There are many things wrong with this analogy, but the most important ones seem to be:

- NAT gateways are inherently stateful (per connection) and IP networks are stateless (per host, disregarding routing information). So even if you only look at the individual connection level, disregarding the host/connection layering violation, the analogy breaks.

- NAT gateways don't actually route/translate by (IP, port) as you imply, but rather by (source IP, source port, destination IP, destination port), as otherwise there simply would not be enough ports in many cases.

Routing of this additional /16 is more tricky and non-uniform though. NAT, hole-punching, all that.

You're thinking of TCP or UDP. IP does not have ports.