People (like ISPs offering routers) set up NAT, often justifying it on the basis of security. Application developers use hole-punching techniques to get past NAT (including stuff like UPnP that requires cooperation from the NAT).

The end product is:

#1 A sandboxing system that cannot reliably sandbox.

#2 A connection system that cannot reliably connect.

So now you have two problems.

NAT is not a security measure but a way to save on IP space or avoid remaking a topology on network addresses changes. For actual security you need a firewall