I too use two laptops. One is personal and the other is my employers. I usually have four displays running in my home office. One for the security cameras, the laptop in primary use will have dual displays and the second laptop will have a single display (often the built in display). I use a wireless full-size key board and mouse on the most active computer. During my working hours the most active computer is my work computer but I shift to my personal computer during my non-working hours.
A desktop (under the desk) computer would be less convenient. It would be redundant for work as I would need the laptop for travel and working from home since I must work in the factory at least some days of the week.
An innovation I have not seen but that would maybe be beneficial would be a (tiny) portable desktop. It would be a box with all the functionality of a laptop (USB ports, HDMI ports, memory, solid state hard-drive, Wi-Fi, etc.) without the batteries, keyboard, track pad and display. Could be sold stand alone or with a set of compact (and/or not compact) accessories like external battery, display, trackpad/keyboard, touchscreen, DVD or other external drives. Maybe even a docking station, do you remember those? I already have duplicate power supplies, wireless keyboard/mouse and displays at work and home so I don't have to carry those around.
This would be very nice for me so that I would not have to take a (bulkier) laptop too and from work, I could take just a small black box. I imagine this box these days would be smaller than my old external hard-drive.
I envision the days of brief cases again. Laptops killed the brief case because they were too big and heavy. You need a shoulder strap to carry them very far. Hell, now it is a full grown back pack. I would not mind a small built in screen but prefer it be separate. If my tablet had more ports it would do.
TEK