There are people who feel this way, that's why most players chose Nord as their first character. To me it doesn't matter and I noticed that roleplayers usually don't have a problem with creating a non-Nord Dragonborn - you're the one who invents the story, after all. My own 'canon' Dovahkiin is a female Imperial, her story is very consistent and makes sense within the universe.
You should remember that there's no such thing as a canon Dovahkiin. Bethesda never reveals the race, gender or profession of the protagonist (with the exception of the Nerevarine, but even then it's debatable) - who you are doesn't matter, what you do is important. You can be absolutely anyone and it won't contradict the lore or non-existent canon. The posterboy is just marketing, it would be difficult to showcase the Dragonborn as a genderless, raceless person

Could be done if everything was showed in first person view, but that may not be the best marekting strategy.
As for magic, well, it's not so simple. It's not that Nords are incapable of magic, they just distrust it - but some of the greatest mages in Tamriel were Nords, just look at Shalidor. A Nordic youngster is much more likely to become a warrior than a mage, but is it so incommon in the real world to choose a different path than your parents envisioned for you? It takes courage and an open mind to become interested in magic after being brought up in a non-magical environment, but
someone had to build the College of Winterhold, right?
For the record, I've never played as a Nord in Skyrim (or in any TES game, for that matter). Never saw a problem with it.