Yes it's two fold also. MF is CCD which AA filters are not needed. Now we may have to check with the scientist on this but from my understanding CMOS also needs to have a AA filter regardless of Moire which also help in noise area's.
I'm not a scientist, but I was selling/advising about the use of Kodak scientific materials to the industry more than 30 years ago, so maybe that counts a bit. CCD or CMOS has nothing to do with the use of Optical Low Pass Filters (OLPF or anti-aliasing filers). It only has to do with sampled imaging with a regular sampling pattern.
It is common knowledge in Digital Signal Processing (DSP) circles that in order to avoid aliasing, one needs to low-pass filter the signal before it gets sampled. The only way to do that, is by fitering the high spatial frequency content that creates aliasing out. The problem with optics is that if we would completely eliminate the possibility of aliasing, we would also lose a lot of high frequency signal modulation, micro-contrast. Therefore most optical AA-filters are designed to only reduce the risk of aliasing, not eliminate it. Therefore the micro-contrast is reduced less, and can usually be restored quite well by proper (deconvolution) sharpening while eliminating most aliasing artifacts.
Noise reduction is not involved, but you probably referred to micro-lenses which are something different.
This we have to look into to get a proof positive answer but the point about Moire and 100's of thousands of users having to deal with a moire issue is something Nikon and Canon do not want to be involved in , so in essence they want to reduce it as much as possible to eliminate it. MF is targeted to a much smaller audience for one and also CCD is all that is used for MF.
I don't think anyone wants aliasing artifacts to spoil the fun. It just happens to be the case that manufacturers of larger sensor arrays don't include an AA-filter. That is not because they wouldn't help the image quality, but it's more about cost, and issues one may run into with oblique rays striking the OLPF at an angle and creating a longer travel path through the filter. Lenses for 35mm DSLRs are usually designed to have limited 'obliqueness' from the exit pupil (e.g. retrofocus wide angle lenses), which helps to reduce light fall-off, color cast, and spatially variant AA-filter effects. Probably the same reason Leica avoids using AA-filters, not for quality, but out of design necessity. So by avoiding the use of AA-filters, they save cost and avoid some other design challenges. The only thing left is to promote (spin) the lack of an AA-filter as a better solution. Unfortunately many fall for that marketoid speak. I'll repeat it once more, Aliasing is no good, but for larger sensor arrays one is stuck with the issue (just ask someone involved in shooting fabrics, or masonry, combed hair, or other periodically repetitive structured materials and lines, at an angle).
Now some things to get answers that may also have reasons for being on MF only as well that may come into play. I don't want to answer them but here are some questions that put more on the reasons why things are like they are
CCD can be made in smaller runs and bigger sizes?
CCD manufacturing is a smaller scale operation requiring dedicated machines. Lower volume and less synergy results in higher cost. CMOS production is a more common procedure (just like the zillions of memory chips that are produced with the same basic equipment) and thus is cheaper to do.
Technically there are some interesting differences between the resulting light sensitive sensor arrays. CMOS devices use much less power, and as a result don't get as hot as CCDs do. That helps in the battery consumption and reduction of thermal noise (especially at long exposures). CMOS devices have another interesting property that can be exploited for photography. The signal of each sensel, can be individually read-out, and it can be done multiple times (allows to reduce read-noise). CCD's off-load the signal destructively, in a bucket brigade type of flow, so a single poor performing sensel will influence all that follow. Hence a much lower yield in production, and higher cost.
CMOS is controlled by mostly OEM manufacturers themselves. Ergo Canon ?
Sony also produces CMOS sensors and there are others, but it may have to do with Canon's huge research effort and the resulting patent position. They are also manufacturers of the equipment needed for the production of sensors (e.g. wafer steppers
There are no real size limits to either technology I know of, other than practical ones like cost/yield/and the need for stitching multiple structures due to photo-lithographic dimension limitations.