What makes a ROM hard? I'm ignorant of the details of chip design, but I'd expect just a large array of essentially open or closed connections. Is that incorrect?
Qwen 3.6-27B is 56 GB of weights. Let's round to 550Gbit. NOBODY makes huge ROMs in modern SoCs, but if we assume it is as dense as the densest TSMC N3 SRAM, this is 33.5 Mbit/mm^2
Then your weights are 16,400 mm^2 !!! The maximum reticle-size N3 die is ~800 mm^2 so you cannot make it.
But, you might say, SRAM is 6 transistors. ROM might be just one. So 1/6 of that... 2730 mm^2... which is still too big to manufacture.