If an Orc warrior being arch-mage bothers you, then don't do the questline.
Many people simply want to be able to do the various quests without a dozen different specialists, and Bethesda don't need to put "rules" into the game that the player is able to do themselves.
What if your character was a battlemage who was equally skilled in magic and combat? Should the game detect what skills your character is using prior to removing the barricade from the doors of the guild hall? If a character wouldn't naturally do something, it's up to the player to decide whether or not to stay in character or to proceed anyway.
Exactly.
If it bothers you that much, RP around it and make it happen, or don't do the questline.
One way to look at it is, that your character is the dragonborn, and therefore a leader. A leader doesn't necessarily have to know every spell. He needs to lead those below him.
If you ever follow real world news, how many times each year do you see some large corporation fire its CEO, and hire a new one - who more than likely - doesn't have any background in the company he/she will be CEO of.
That's because that person has college degrees (Probably at least a masters degree), and has done enough work in real life to know what it takes to lead people from the top, regardles of what the company does. During the times when he/she needs to make a decision about what direction the company should take, he/she gets advise from all the people below them - and then make the decision. The only way to fail there, is when people below you provide you with wrong or incorrect/inadequate data. This should be pointed out by the others (hopefully), and then - eventually - you fire the person that gave you the incorrect information and move forward.
I know this is a simplified version of what happens, but being in charge doesn't necessarily mean you have to know everything (of course, there are exceptions, because there are companies where you do need indepth knowledge).
It just means you have to lead.