You’re incorrect that shouting was just a normal things all Nords could do. The PGE pretty explicitly says that shouting is a dying art outside of the Greybeards and a few other enthusiasts:

But, alas for the Nords, one of the mightiest of all the Tongues, Jurgen Windcaller (or The Calm, as he is better known today), became converted to a pacifist creed that denounced use of the Voice for martial exploits. His philosophy prevailed, largely due to his unshakable mastery of the Voice -- his victory was sealed in a legendary confrontation, where The Calm is said to have "swallowed the Shouts" of seventeen Tongues of the militant school for three days until his opponents all lay exhausted (and then became his disciples).

Furthermore, we never see Nords shout in any of the previous games, which you think they would’ve done if it was a common thing for experienced warriors.

Personally I don’t think they need to have an entire extended Bard’s college questline, though I would’ve liked that. I was just giving it as an example of them displaying previously established lore. I do like the Bards are a prevalent and respected profession in Skyrim though.