To expand on what rowdy said:
Most notebooks have scissor switch keyboards, which are about 1/2 cm high at most.
The modern laptop keyboard module is about 6mm thick from top of keycap to backside of plate (really a semi-flexible metal sheet). It's pretty amazing you get 2mm of travel from that total thickness, though it cheats a bit by relying on the rest of the laptop to provide most of the rigidity needed.
Not sure about MY switches, but MX switches are much higher than that, and then add the keycap on top of that.
For comparison, the ML switch module itself is 9.6mm (for 3mm travel) and the MX switch module is 18.5mm (for 4mm travel). Neither of these include the keycap thickness above the stem or the required rear covering (since they're both through hole PCB mounted switches). For comparison, my relatively fat little Lenovo X220 (a 12.6" subnotebook, but definitely not an Ultrabook) has a base thickness of ~19mm in the keyboard area not including the screen, or 25mm including the screen. The HDD and motherboard are almost entirely located under the keyboard. A MX switch plus keycap is about as thick as the notebook is when closed.
In short, to use MX switches, you'd have to be OK with a 2" thick laptop without being able to use that extra thickness for better cooling or more expandability (though you could stack a couple HDDs/SSDs in the wrist rest area).
