I know this is humor, but for the record this wouldn't work. Each simultaneous TCP connection needs a unique four-tuple (source address, source port, destination address, destination port). If a lot the people behind the NAT try to connect to the same place (destination address and port) at the same time (something popular like Google, YouTube or Netflix), and their source address is the same, the source port needs to be different for each connection. So after at most 65535 connections within a short time the NAT would run out of ports and no one behind the same NAT would be able to open new connections to the same place until the NAT mapping expiries.

So you could have at most tens of thousands of people behind the same NAT, maybe even fewer to make it reliable.