Without NAT, you can do hole punching. A third server can coordinate two peers sending packets to each other to make their firewalls each see the connection as outgoing and allow traffic. With NAT, the peers don't know which port they're sending on, so they can't relay that info through the third party (though maybe you could have one port scan the other).

Also, an application can use upnp to configure your router/firewall to allow traffic. You could do that with NAT too I suppose if ISPs allowed that, but you'd be contending with other users if you wanted a specific port like 80.

Not really? No need to mess with destination ports, no need to visit whatismyipaddress.com, no need to risk exposing your entire home network through SIP ALGs, and your Xbox/PlayStation doesn't tell you that you have a bad "NAT type". Plus, when you forward port 1024-65535 to your Nintendo Switch, as Nintendo says you need to do in its documentation, the rest of your devices don't have their P2P network traffic impeded.

> when you forward port 1024-65535 to your Nintendo Switch, as Nintendo says you need to do in its documentation,

Nintendo is a shit company that treats their customer base like bitches yet gets a tremendous steady amount of good will solely due to nostalgia. I'm the last to want to defend the challenges that NAT brings, but blaming it due to some rando corporation's asshattery is silly. Luckily, or not, their documentation is wrong, you almost never have to blanket port forward all UDP ports for the Switch.

The GP point still stands as well. If you have a firewall set to block inbound by default (typical) you have the same basic port-forwarding bootstrapping/configuration problem. Also, the reasons you would absolutely need whatismyipaddress.com or similar apply to both v4 and v6. If you're configuring your router anyway you can get the v4 address.