Why is there no flat mechanical keyboard?
Solution 1:
They do exist. They are just hard to find.
I love mechanical keyboards, but they are too high, which forces you to place your hands/wrists at a very unhealthy angle.
Here is a flat mechanical keyboard (the "Rapoo KX"): http://www.pcworld.com/article/2860856/rapoo-kx-review-the-mechanical-keyboard-enthusiasts-tiny-traveling-companion.html
Company's website: http://www.rapoo.com/ProductShow.aspx?PType=CHTi%2f0TqNIc%3d&PID=uCupl3PJuVw%3d
There is also a discussion about them here:
http://deskthority.net/workshop-f7/flat-key-caps-progress-thread-t8415.html
https://geekhack.org/index.php?topic=60531.0
http://www.mmo-champion.com/threads/1292723-flat-key-mechanical-keyboard
Solution 2:
If you ever take apart a laptop, you will notice that although thicker than non-mechanical keyboards, they can still make mechanical keyboards to be quite thin. The following keyboard (the one in my primary laptop) uses scissor-switches, which although I don't have the exact dimensions for, would estimate results in a keyboard thickness of about 8 mm: https://www.youtube.com/watch?v=Ci0kNZvoqKQ
There is one problem, though: the aluminum plate on which everything is fastened does give a bit when bent. "Flexible" and "mechanical keys" don't go well together; a mechanical keyboard inside of a backpack getting slightly bent is more likely going to get permanently damaged than a membrane keyboard. (In fact, since membrane keyboards are happily bent, you can even create keyboards that roll up, something that would be impossible with mechanical keyboards)
If you want to use a scissor-switch keyboard as an external keyboard, the primary hurdle would be securing this aluminum plate in such a manner that it doesn't bend, which would require a plastic enclosure, adding to the thickness of the keyboard.
And in the end, most mechanical keyboards (or at least the ones I would take apart as a child) use the exact same principle as a membrane keyboard, but instead having each switch covered by a "plastic mechanical shield" that gives different feedback when depressed. So if you want to make a keyboard as thin as possible (and cheaper!), just remove the mechanical plastic bit entirely.