Surely that added flexibility negatively impacts the density/parameter count of the model you could etch?

I think they already do that, except it's not 1980 so you don't fix the upper mask, you fix the lowest metal layer (the upper layer is very coarse and is only useful for power). But even a single mask is still quite expensive.

But I suppose the interconnect masks don't have the resolution requirements of the masks for transistors. Therefore it could be a lot cheaper.

(Yes, you could fix a number of masks, e.g. entire logic gates, of course).

Or do a hybrid