Sure, there's false detail, but false detail is just that - false. To me it looks like fine grained noise, or, if on edges, jaggies, neither of which are desireable.
What I find so obviously false about aliased imaging is that I can clearly see that the image is composed of pixels. I don't want to see that an image was recorded in pixels when I look at it.
One of the problems with aliassing as once it's in a system it's very hard to remove as it's practically impossible to know whether detail you see is real or not, and hence it's hard to remove the detail that's not while keeping the detail that is. That's why most cameras use an OLPF as a lesser of two evils.
Finer pixel pitches are the solution - when you get fine enough, you don't need AA filters; everything the lens can do is there in all of its glory, without aliasing. Reading out a 250MP sensor is not an easy chore, however, with current technology and storage mediums. Hopefully, one day, we will have that convenience, and cameras can have settings to downsample the data as the user wishes, or even have automatic MTF detection systems, that examine the image before writing to the card, to see if there is anything worth recording at maximum resolution, and automatically picks the highest resolution for a downsample that the recording warrants, and only writes out the lower resolution to the storage medium, as a linear DNG or something similar. There could even be zones with different resolutions, to save storage space on bokeh.
I think this is even more important on moving images than stills as on stills, theoretically, if you've got the patience, you can go in and pixel paint out some of the problems. I certainly can't be bothered to do that and prefer to use a camera with an OLPF.
Of course, there's more to resolution than OLPF or not. Not least the fill factor of the pixels, lens and bayer reconstruction algorithm used.
Indeed, stacking photon detectors on top of each other is rather clever and allows for larger pixels. However, silicon is not the best colour filter, and it's the extreme matrixing needed to transform the layers into RGB that limits the noise performance of the Foveon.
It is, however, an excellent way to do greyscale. Foveon RAW data, treated as two channels, "red" and "cyan" ("blue" + "green") are fairly low in noise, as is their sum. The biggest problems are between the "blue" and "green" layers, where color must be extrapolated, boosting any noise, and there are blotches of a complimentary effect, where the green channel is dark where the blue is light, and visa-versa, especially in shadow areas: