Now, what I want is for someone to build the old Northgate OmniKey Ultra keyboards. Function keys on the left are so useful for many purposes and I especially like them because I can reliably touch-type the ones on the left but I can't reliably touch-type the ones on top--they're just a little bit too far away, I sometimes miss.
I used an Omnikey for a while recently-- nice solid board, and agreed that the layout is nifty, but I've had nothing but trouble with the reliability of modern Alps-like switches. Right now, there's a GH-122 on my desk (one of those enthusiast projects from like 2016)
A few gaming-design boards, have extra columns for macro keys which could be remapped to function key layout.
low-travel key switches used to be popular on CNC machines to reduce chances of machining-chips/debris getting into the keyboard. The key caps also used extended skirts to bring the cap as close to the PCB as possible. (example : http://www.calmotion.com/images/keyboard-1784-P_0h93fj2n.jpg )
Membrane keyboards and touch-screens have basically replaced any real switch in machining environments, but maybe a DIYer somewhere would find some use in those kind of environments.
On an ANSI keyboard, a single function key could toggle the numpad's 1-9 keys into F1-F9 keys, and have the additional 3 on top be F10-F12. That might give you an experience similar to the Omnikey's side F keys, as long as you're OK with having them on the right side. Might work better if the arrow keys and nav keys above it were removed so that the Numpad would be quicker to reach, since the Num Lock key makes them redundant anyway.