why so quick to say No?
Sony and Valve could very well go into an agreement such as this:
think about PSN+ revenue share! with Valve! in exchange Valve exclusives on the PS4 only along with Valve's steambox! if PS4 was to get HalfLife 3 along with the steambox Valve would still be able to sell the software but now on also a big three game console and make not just profit but also revenue share on top with PSN+ !
Who said the PS4 wouldn't get Half Life 3? It might. It just won't be a Steam Box. Is the PS4 running Linux? Can I install Windows on the PS4 if I want to? Can I mod the internals if I want to? The Steam Box is a plethora of Linux computer systems shaped like a console, not a proprietary console made by Sony Corporation.
that is why there is thing's like virtual machines, remember streaming Technology is just now getting to be a driver in all three main box'es moving forward!
IF, this is a big If, the next PS3 is a SOC x86 chip like the rumor's already stated, a STEAMBOX virtual machines Application could indeed be made, who said anything about installing another OS? you do not have to have that functionality in order to be a steambox, the PC standard is not a steambox based on what kinda OS it has, its a steambox based on the software infrastructure! its a platform agnostic approach! just like Sony's Playstation Mobile development platform, its also platform agnostic in its design. I would not be so quick to count this out, the simple reason right now out of the big three only Sony has let Valve have a foot in the door with Valves steambox software infrastructure!
Not Nintendo, or Microsoft have done the same.
Also, this is not out of the realm of an idea i would imagine because:
playstation 1 linux kernel loader
playstation 2 linux kernel loader
playstation 3 linux kernel loader
playstation Vita also has a linux kernel loader
every Playstation has had one and virtual machines are just as much a viable option to use as anything else. Now not every game of course but with streaming technology improving we may see more parity of a game centric streaming game service added to playstation 4 can be such a start, adding Valve as yet another such added services would or could not be out right a No! I am of course not saying it will for a fact, i am saying this could very well even be a feb 20th Announcement!