I realize this post is over 5 years old, but it's worth revisiting.
My ideal setup is the one I have now - a single LG 38" curved monitor with two inputs permanently wired, DisplayPort and HDMI. The desktop computer is connected to the DisplayPort, and the HDMI cable is connected to the monitor but left dangling at the other end (typically used for a laptop). As soon as I connect a 2nd device to the HDMI cable, the monitor pops up a menu asking which input to use, or both. If "both" is selected, the monitor goes into split-screen mode and displays both computer's video side by side.