The designers of the internet made one fundamental mistake, namely applying meatspace norms to cyberspace.
In the "real world", you don't really need that much security. Your actual security comes from the fact that all the worst criminals are already locked up, most of the would-be criminals are afraid of being locked up, and if somebody does actually commit a crime, they will get locked up and won't be able to do it again for a good while. A lot of real-world security is about post-factum detection (think alarms, CCTV, panic buttons etc), because in the real world, detection and prevention are two sides of the same coin.
This only works because if a real-world crime happens, the criminal by definition is in the same location as the victim, and law enforcement cares most about the community they serve. If the criminal is across the world, as is the case in cyberspace, even if it's a friendly country, it's often "not their problem". This means internet systems need actual security, and NAT provides exactly that.
If not for NAT, we'd all need a firewall, and things would be almost if not exactly the same. In the real world, "leave things relatively open, because locks are mostly for keeping honest people honest" is a valid strategy. This strategy doesn't work on the internet.