I'm looking at this more from the 'Bethesda opened a can of worms' angle than storyline. I'm sure plenty of TES fans wouldn't mind going back into the shoes of a 'normal' hero/oine, however for the majority of players who bought Skyrim but arn't deeply invested in the series as a whole the draw and focus of advertising was dragons... and the ability to use dragon-shouts. To the point that Fus Roh Dah has become a massive meme. And I don't doubt that many longtime fans love it. It comes from the lore, is fun, and there was even an Oblivion mod that allowed the PC to use Shouts.
It's being made into such a big part of the gameplay, and become accociated with the TES name, that 'removing it' for the next game might lose that game sales. I imagine there would be plenty of low reviews purely because of it. Petty, but they would happen.
I'm not saying I support such thinking. I personally wouldn't mind being a 'normal' character again. However, I certainly wouldn't blame Bethesda is future TES titles had the Thu'um as much a vital part of gameplay as normal magic, melee and ranged. I'd certainly download mods that re-allowed it as an option. I'm just pondering whether keeping it as a basic feature might not be the safest option, since for longtime Skyrim players it might feel like lacking a limb to no longer have it in, say, five or so years time of playing with it.