Honestly I think you don't understand what NAT is.

Stateful firewalls basically work by watching your connections and then allowing the return traffic through. All firewalls are stateful, there are "stateless ACLS" in networking which are stupid and don't watch things; we're not talking about those ... in fact 99% of internet users will never interact with a stateless ACL.

What happens when you make a connection is that your router adds your state to it's "state table" _and_ pops open a port on your gateway to allow return traffic through, if you did not have a stateful firewall in place then the whole internet would be able to poke that port.

If you remove the NAT the only thing that happens is that your router doesn't have to pop open a port and route traffic from that port to your device, the stateful firewall stays in place, meaning that random devices on the internet CANNOT TALK to your internal network at all, unless you manually allow that, which is the same as what happens with port forwarding today.

The only thing you "lose" is that your whole house looks like one device.

You gain a significant reduction in latency, online games will work better and p2p networking (such as voip) will have significantly fewer problems, because the whole internet was designed without NAT in mind, because NAT is genuinely a terrible hack.