nyquist's sampling theorem is from 01915. western union started offering wirephoto service in 01921, and the associated press started mass distribution of news photos in 01935. these aren't discrete pixels but they did demonstrate that nyquist's sampling theorem applies to images too
If you want to use that sampling theorem, you have to bring up frequencies. Explaining those and how they apply to printer's ink is arguably more complicated than what Turing did; especially for his contemporary target audience.
The argument from pixels is more natural to us these days, that's why we think it's simpler.
(I had similar reactions to many other older style proofs when I was studying math.)
