What limitations exist for high megapixel pictures being used as magazine covers due to printing materials, and technique?

I’m sort of not answering your question directly because I haven’t dealt with magazine covers personally.

However, it depends on the magazine—if you look at a NatGeo for instance, you’ll see a much higher quality printing process used because the mag is as much about the photography as it is about the articles. And NatGeo held out against digital for a VERY long time.

Most magazines have embraced digital photography, which means making due with less pixels, but it ends up not mattering in the end because of the relatively low-resolution printing techniques they’re using.

The Canon 1D Mk II has been a mainstay of magazine shoots—at 16.7MP it barely gets you 11×17 at 300dpi. For comparison, 35mm film gets you 20MP, or about 12×18 at 300dpi. For fashion work, medium format (80+MP film or 40–50MP digital) has been the typical format, but those are often getting blown up to billboard or kiosk size.

Offset commercial printing presses use four basic ink colors: CMYK. Each color of ink is applied separately – one plate per color. Small dots of the four inks – cyan, magenta, yellow, and black – are deposited in specific patterns that make our eyes believe we are seeing a wide range of colors. That’s why the standard offset printing process is often called 4-color printing.

The size of the dots and their spacing will determine the resolution of the printed picture. It will never equal photographic reproduction, but is far less costly for mass production.

Depends on the quality of the magazine and perhaps whether the magazine is oriented toward the arts. They will use a higher dpi ratio say 400 dpi, average magazine maybe 300 dpi, newspaper 200.
As@jjewel says above, the processes are totally different, rgb for photography, cmyk for pr

See this article for useful details concerning the relationship between original digital photographic imagery and printed images.