You still need a firewall regardless of NAT. Otherwise, every time you take your computer outside of your home, you're no longer protected. Any attacker or compromised device on your hotel, airport, or coffee shop wifi network would have direct access to your machine.
There's probably a field of study with vocabulary and accompanying proofs of significant rigor that prove or disprove this. Maybe they'll stop by our little subthread and clear it up.
A NAT implementation could broadcast any "WAN" side incoming packets to all link local clients (aka: put everyone in the DMZ). The only thing preventing that is a stateful firewall.
This is a very common misunderstanding. NAT and firewalls are separate concepts. You can also have NAT with no meaningful firewall -- a port remapping NAT that allows anything through.
Most IPv6 networks are firewalled but there's no NAT.