PiP, PbP… a dual desktop solution?

I’m still pondering desktop setups, but I have had what I think is a genius idea (like all my ideas, obviously 😉 ). If I get a monitor with dual selectable inputs, and better yet one with picture-in-picture and picture-by-picture, I can connect up both the Desktop and the Laptop to one monitor and switch between them as I need. I can have the best of both worlds… but still have a sync’s issue. Hmm. Further thought needed.