Firewall is a feature. Forced NAT that noone in the above described situation wants is just a flaw. And the other solution where you're forced to buy a fucking "public" number out of a grossly insufficient pool of those for $5/month for each of the NATted machines and your router, is a crime against humanity.
I'm naive with network security, so this is a honest question looking for a practical honest answer: Would my grandma's computer, with its old version of windows, be more or less safe with a NAT without DMZ configured?