Why do we need to simplify our games? You mentioned about being able to play games with others, so why not play a co-op arcade game?
Taking out the dual-analog for modern FPS won't work. Its a wonderfully proven system that makes sense and works.
Limiting to one-button takes out all of the perks and wonderful features added in to modern games that make them more interactive, more realistic, and more fast-paced. Not to mention all of the quick-time events would be thrown out.
The fire or use button will always, ALWAYS, need its own button, no matter what. Attaching a menu to that same button would make for a really complicated and slow system.
The concept itself isn't workable for the games coming out nowadays, however the idea is nice. I think a two-joystick, two-button approach would work better if in the right hands, but really, in the end, having a wonderful loadout of buttons means that several different options are always available, and in the games out today, running around shooting the same gun until it runs out, or having to find cover to change it, just won't cut it.