Do grayscale images take less space?

This should end up being true for any presentation image format (the one you're going to actually show people, not necessarily the one you might do editing work on) optimized for human vision as well.

It's more a property of our eyes than a quirk of JPEG. So I don't find it misleading personally.

Not only that but color and brightness are often correlated, and advanced compression techniques use that property, see "chroma from luma" in AV1.

Without compression, indeed, it can be 3x, or even 4x (for alignment).

This got me thinking about how subtle and slippery the concept of "resolution" is.

The relationship is not strictly 3x; an ideally demosaiced Bayer filtered image still contains some information at the original capture resolution, because R, G, and B are correlated in nontrivial ways. Nyquist is a nice and simple result for the special case where nothing can be predicted about the original function, measurements are assumed to be perfect, and the criterion for reconstruction is "exact" - but in the general case of "recovering information, more is better" even a simple interpolation procedure with tame priors like "luminance exists" might perform so much better than the naive approach that we'd be silly not to use it.

Even the Nyquist frequency itself is less fundamental than it first appears; a less well known result is that a function can also be perfectly recovered if sampled at half the Nyquist frequency, if the slope is captured as well as the value. In other words you can losslessly convert a 2MP image into a 1M value+slope data matrix and back. What resolution is it? Depends on your point of view.

https://en.wikipedia.org/wiki/Chroma_subsampling

There are some major failure cases involving alternating single pixel width red / black lines. That caused issues with DVDs because the format also used interlaced frames, meaning things like red tail lights at night could end up looking awful.

Luckily AFAIK they've given up on interlacing.

I really think with modern tech they'd be better off trying to compress 4:4:4 instead of immediately throwing out a lot of colour information.

If it's a full scale photograph full of grayscales that's been dithered, then it's a harder comparison to make. Because obviously a ton of useful detail is lost in the dithering, in a way that isn't with lines and letterforms. So the comparison would really have to be with a terrible, blocky JPEG super-compressed file. In theory the JPEG should win.

This page has a few visual examples at the bottom: https://www.cs.unm.edu/~brayer/vision/fourier.html

It converts the image into frequency domain, and reduces precision of the frequency data, with a special case when the data rounds down to zero.

However, whole-image blur crosses the 8x8 block boundaries, so it isn't perfectly aligned with the blur that JPEG uses. Lowering quality setting in JPEG (or using custom quantisation tables) will be more effective.

There's also a fundamental information-theoretic foundation for this — lower frequencies carry less information.

You can also typically discard high frequency data in your color channels. So not only are you not storing full precision data, you also don’t need to store roughly a third of the frequency bins. You can think of this like cropping the image but in the frequency domain. The data saving are identical to cropping the image but visually imperceptible.