Valve basically tried the later approach with the initial Steam for linux push which included steam machines and the steam controller. It did have some level of initial success but clearly had lost momentum and the developer support it had seemed to fade after a few years. There were quite a few direct ports during that time though. I think they would have preferred that approach but ultimately decided it was a bridge to far.

They didn't put a fraction of the effort into Steam Machines that they have put in the Linux ecosystem since then.

Wouldn’t this hypothetical consortium need to be made up of fairly large players?

As in Microsoft, Nvidia, Intel, and friends?

I’d imagine they’re pretty happy with the status quo.