True and not true. I own few telecine and film scanning machines. Most of older film material, esp. 16mm isn't worth scanning over full 2k. 1556 in y on 16mm esp. important because lots of people want to reframe into 16:9 and 1556 gives more than 1080.

Anyways, most of old stock (print, negative, ip) have grain such that over cca. 2.5k won't yield anything better. However, kodak and fuji stock from mid to late eighties definitwly is worth capturing at higher detail. Highest-detailed stock from nineties we've measured to have spatial rwsolution of around 8.5k and that's about as high as you will get (rare) out of 35mm.

tl;dr; depends on the stock

edit: Here's previous mini discussion regarding telecines, if anyone's interested https://news.ycombinator.com/item?id=11377678

> I work in the film industry, a 35mm full-aperture negative scan holds only about 2048x1556 pixels-worth

There are enough good 4k releases of classic movies to see this is not the case. You can compare the 4k and HD release (which is just under the resolution you provided).

I regularly scan Vision 3 film (movie stock) and Velvia 50 and Velvia 100 (E6). I scan it professionally at 10 Mpix, but when I have a good picture, I pay big bucks to have it drum scanned at 100 Mpix. Yes, it's not 100 Mpix, there's about 15-25 Mpix worth of detail there, but it's much, much more detail than the 10 Mpix scan.

Apologies it does sound[1] like an absolutely perfectly shot 35mm frame can theoretically hold up to 20 million pixels-worth, but I've never seen this in practice in the vfx industry, it's almost always less than the ~3 million pixels that 2048x1556 provides.

http://pic.templetons.com/brad/photo/pixels.html

Some of those classic movies were shot on 65mm and 70mm. Others may have simply been upscanned, which will yield a sharper looking image nonetheless.

The Hateful Eight had a little media blitz when it first came out because you could watch it in a number of theaters that still do 70mm, and I think Tarantino was the reason.