You can compete also without locking games to one platform only. Then the competition is not about being forced to buy a certain piece of hardware to play a certain game, but you select the hardware that offers the best bang for the buck, and still can mostly enjoy the same games as others.
Even the PC is not agnostic. You can't play most games if you don't have a Windows OS installed. It is "hardware agnostic" but not "software agnostic", since you still need a specific OS to run games. I would much rather use a OSX machine if i could, but i'm locked to Windows because most software is written to run on it.
You are promoting a form of competition where e.g. Sony pictures movies could only be watched on PS3/PS4 and Sony TVs, or Sony music could be listened only with Sony-Ericsson smartphones. Competition through HW-locked media is such an unattractive model from the end-user point of view.
The way games work is completely different than the movie and music industry. You're comparing things that are completely different. Games rely much more on specific hardware setups and programming languages than other forms of entertainment. And even then, the movie scene is from being as agnostic as you say. Who owns the Blu Ray format again? Yeah, Sony, and if you want to produce a Blu Ray movie or a Blu Ray player, you need a license from Sony. The 3DO had a similar concept back in the day, it was licensed to many manufacturers to make their own 3DO consoles, such as Panasonic.
The hardware-adgnostic concept, while beautiful in theory, would never work because of how the games market work, at least in my opinion. The hardware market is way too risky and expensive to get into, which is why we only have 3 companies and many have failed in the past. Consoles are sold at a loss most of the time (which doesn't happen with other types of eletronic devices) due to the insane hardware they have to put into their machines to be able to compete in the market while keeping a low cost for consumers. They try to regain their investment through licensing fees and by selling games. This fact alone is enough to put an end to this utopia. Companies won't bother purchasing licenses to sell their games on consoles with smaller userbases.
Also, programming languages are completely different. The Xbox 360 uses Microsoft's Direct3D while Sony uses Open GL on the PS3.
Even "multiplatform" companies such as EA ditch one console in favor of others, like they have just done with the Wii U. My point is: even if Sony, Microsoft and Nintendo drop the exclusivity, there will still be one console that will have more games than the other.
Heck, even the mobile market is not agnostic, we have games for Android, Windows Phone 7 and iOS, each with their own exclusive games.