Axiom

Hmmm. Think I can see where this is heading. Doubt I'll be able to dissuade you but it's worth a go.

The "learn strategy, reflex timing" thing doesn't really hold water in this context. Handing over a switched off controller won't provide any of that. It's more akin to: here hold this, sit there, and do nothing. While I, sit here, and do slightly more than nothing. Not really quality time. Besides that though, it's not constructive because even a four year old won't take long in realizing that there is zero consequence to the buttons being pressed.

Don't understand what stimulus you foresee coming from mashing at a controller to no end, other than what you added about discussing whats happening. And it's not that I'm against kids playing video games and all. Far from it. There are plenty of titles available that provides what you mention and also allows the opportunity for meaningful cooperative interaction. Many of which offer actual educational benefits. So, it's not like I'm trying to begrudge gaming parents.

Can't really point towards a proven case study on the subject. Admittedly, and unfortunately, it's just personal and unquantifiable experience. From which I have gathered, that a kid will look for not only activities that provide appreciable results, but ones for which they can interact with others.

You don't have to be the "Worlds Best Dad" in order to not be a shitty one. And not you necessarily, but before someone comes out with the parent/not a parent thing. I am not so dense as to think you have to had actually reared a child in order to know anything about it. That's just foolish.