To be fair I think the idea of using algebraic number theory to approach the problem had been tried before (Tsimerman mentions he tried a similar approach that the model ultimately succeeded with, but didn’t persist with it.) It’s quite a general trick to use algebraic number theory for constructions in the plane, as you have the lattice associated with the ring of integers of number fields.
I personally am blown away by the proof but it would be far more impressive had it come up with a novel connection between fields, or indeed if it had turned out there wasn’t a counterexample and it proved a tight upper bound (See Gowers’ initial reaction.)
My model of things is that there is a core set of generally applicable research skills, and then there is topic specific technical knowledge required to conduct research in that particular area.
I don’t think models are bottlenecked by technical knowledge. I think they just don’t currently have the general capability required to do broad exploratory research, outside of narrowly specified verifiable problems.
I would guess all these subfields will get automated at the same time, once said capability is developed.
Different groups have specific agendas, and within said agendas you can try to automate the production of incremental papers (which are important!) But in the limit you’re going to have to develop concepts beyond the current frame if you don’t want to stagnate, which requires general exploratory research ability.