Even if NAT always implied a firewall, that doesn't change that the NAT is not the thing that is keeping you safe. The firewall is what is keeping you safe. That's why you don't need the NAT to stay safe. You can just drop the NAT and keep the firewall and everything will be fine.
You might as well say that a car radio keeps you safe in an accident. Because a car with a car radio for practical purposes nowadays comes with an air bag! Yeah, sure it does, but it's just nonsensical to conclude from that that the car radio is what is keeping you safe. It's not that buying a car with a car radio isn't a way to keep you safe in an accident, it's just that the car radio is completely irrelevant to the problem. Buy the same car without a car radio and you will be just as safe.
In the real world SOHO routers that implement NAT also include the absolute bare bones firewall functionality of "block private addresses on the WAN port". Hand wringing over "but if someone convinces my ISP to route a 192.168.x.x packet to my home it could bypass NAT!" is pointless.