I'm amazed at how many people missed the OP's point (at least as I understood it).
1) Skyrim is a great game
2) Many players feel like Skyrim is not a true "open world RPG" when stacked up against open world RPGs of the past.
3) Can the open world RPG genre exist today or is it dead/dying?
It wouldn't be the first genre to die. Horizontal/Vertical Scrollers are a mostly dead genre because of the graphics change. The shift to 3D did not "improve the genre" it created a very different game. Compare Super Mario 3 to Super Mario 64 (the first 3d mario), they are not the same even if they are both "platformers". As are top down RPGs like Baldur's Gate, I thought Dragon Age might revive this... then we got DA2. Every so often we get games that prove these genres don't NEED to be dead. Dragon Age: Origins is the perfect example. It was basically a return to games like Baldur's Gate, or Icewind Dale. It did really well for itself but they decided DA2 needed to appeal to a larger audience so it's not so much like Baldur's Gate or Icewind Dale.
I think the Open World RPG genre could very be dying at this point. TES isn't the only open world RPG series although, the Gothic series already showed it's going seriously towards action/adventure with ArcaniA: A Gothic Tale (aka Gothic 4... so mad about that). I'm definitely concerned that before long open world RPGs will be replaced by "Medieval Grand Theft Auto" and finding a good open world RPG will be like finding a good turn based strategy game.
I think most RPGs, not just open-world ones, are suffering. You already brought up BioWare's unfortunate lack of RPG anything, anymore, and although there are companies that still create some great RPGs against the standard, many are suffering and the RPG genre is so relatively scarce and rare among the multitude of shooters and action games vastly preferred by the public. JRPGs no longer line the PlayStation shelves. WRPGs no longer line PC shelves. RPG series left and right are getting less choice, more streamlining, and more action. Dragon Quest is unfortunately moving towards the MMO scene, Final Fantasy XIII was just a disgrace... a pretty, but highly linear and monotonous disgrace. BioWare's pretty much a lost cause with Mass Effect being just a third-person shooter now getting multiplayer and DA II just a rushed, rehashed action game. Gothic's just gone. Skyrim has barely any choice and cut out quite a few details of its own, although TES games post Daggerfall tend to be like it but it's gotten progressively worse. The RPG is suffering and while still technically alive, it's not nearly as popular as it used to be and the genre is a shadow of its former self across all platforms. However... Final Fantasy and Dragon Quest used to be open-world RPGs, so maybe it is mostly open-world RPGs...