I thought DRAM was pretty dense already. Is mask ROM that much denser?

Yes, each rom bit can be a transistor or even a diode with a decoder circuit. Simplest Dram cell is capacitor+transistor - and you need a clock, refresh circuit etc.

Someday, I imagine model weights could even be encoded as analog resistors (memristors or similar) for even greater density

Hm. I wonder how many relays I'd need to make a physical MNIST classifier. That'd be dope