Yes but wasn't there a time when many Nords were proficient in it ? During Alduin's Bane those three Nords all used the Dragonrend shout. Which at least shows it was a more common power back then. Surely given time many Nords could be trained to use the Thu'um again, which would give them an advantage in fighting the AD.
Sure they could be trained, but again, who's gonna do it? The only ones with any experience at it are the Greybeards, and they're not returning your calls.

I'm not saying it can't happen, but if it does you're looking at a very longterm program, not some solution to the Dominion threat that's gonna be readily available any time soon. There are only two people that we know of in 4E 201 who know how to Shout and are not Greybeards, the PC and Ulfric.
The PC has no experience in teaching others to shout, and I'm gonna say that being Dragonborn would be a disadvantage here because the PC has never had to learn
how to do it at all - the ability is inborn. The Dragonborn only has to learn the words of power and attain the full knowledge of what they mean in their magical context as part of the various Shouts, and this also happens naturally by virtue of being able to absorb that knowledge in the form of the souls of slain dragons. Other people don't have those options, they have to learn
how to shout, the actual mechanism by which those words can be transformed into a kind of magic. The Dragonborn doesn't have the first clue about that because in his/her case it's never been needed.
And as far as we know Ulfric has never trained anyone else to shout in all the years he's been out in the world with the opportunity to do so. I will say again, if he could do it all, and wanted to do it, it would already be happening. Or maybe he feels that his own personal "blasphemy" in using the Thu'um for combat purposes is enough of a weight on his conscience and doesn't want to stray any further from the path he was initially taught than he already has.