If it did then you might have a point, but since it doesn't it's very different from a firewall that's configured to do that.
That's the primary function of NAT, not a side effect.
> It doesn't filter incoming traffic.
Of course it does, it drops any incoming traffic for which it cannot find a corresponding connection. How is this not a filter?
I know that internally these two are vastly different. The reality is that NAT is used as protection for millions of home networks.
Well, no. They do ignore them, but that's not effectively a drop. It's an ignore. It just means that they don't edit the packet. Whether it gets dropped or not depends completely on the routing and firewalling parts of the router.
People do generally expect a NATing router to firewall inbound connections, but it's important to realize that you won't get that behavior from NAT. You must have a firewall, which is a separate thing.