No, the truth is somewhere in between. You're partially right, but you're missing a few things.

Regarding spatial sampling, bringing up Nyquist is mostly a red herring, because you can make the same exact argument about the discrete pixels of monitors as you can about sensors. So one pixel of sensor is as good as one pixel of monitor, for this purpose. However, when cameras use optical low-pass filters (anti-aliasing filters) to avoid aliasing effects on the sensor, this does reduce the spatial resolution of the sensor slightly (due to the impossibility of a perfect brickwall filter), slightly reducing the information content of each pixel (because pixels are correlated with their neighbors, therefore knowing the neighbor provides partial information about the pixel).

Regarding the Bayer filter... yes, it's absolutely true that each color is sampled at a lower resolution (in the classic RGBG filter, 1/2 linear resolution for red and blue, and 1/sqrt(2) linear resolution for green). And this necessarily decreases the maximum information captured by a Bayer-filtered sensor of a given pixel dimension, compared to what could be displayed by a full-RGB monitor of the same pixel dimension.

But it's important to remember that the scenes we photograph aren't maximum-entropy sources. To whatever extent the scene contains mostly low-frequency information, below the Nyquist rate, the AA filter removes very little information — and mostly they do. To whatever extent the color channels in a given patch of the scene are correlated in a predictable way, the Bayer filter removes very little information — and mostly they are. So the information-theoretic "effective resolution" for an image sensor photographing ordinary scenes is much higher than what you calculate it to be. Without any real mathematical backup, I'd say that it's probably 75-90% of the raw pixel count, not 8%.

Given this, and the lack of any supporting evidence (and the aspect ratio difference pointed out in another answer), there's no reason at all to think that the prevalence of 24MP sensors has any relation at all to 1920x1080 monitors or 1080p video formats. More likely, it's just a convenient place where manufacturing technology, consumer expectations for decent photos, and price all come together.