Maybe the problem is...
Where we keep our monitors today.
Maybe instead of standing up vertically at the back of our desks, they should be closer to us and at an angle more parallel to the surface of the desk - you know, in the kind of orientation you hold a textbook when reading it... at about desk-height, with the top of the book angled a little bit higher than the back of the book. The keyboard might be on a shelf beneath and just slightly in front of the monitor.
And then when people come to your desk, the desk surface would be clean, as opposed to having them sit on the opposite side of a wall of monitors.
Things are in a period of drastic change right now - and your argument against touch-screen desktop systems isn't very visionary. If touch is superior enough, maybe the paradigm for desktop PCs needs to evolve completely. The monitor on our desk is the artificial barrier that limits productivity - not our inability to hold our harms straight out for extended periods of time.