I also play D&D and Morrowind is my favorite TES and I roleplay but I've managed to do all guilds with one character just for the kicks. As soneome who mentiones tabletop gaming you should be able to find a way to disregard some things or should be able to find an explanation for it. As for some things you say, why wouldn't warriors be able to cast spells, sure they ain't gonna be spells that full-fledged wizard will cast, but still. And no, Companions are not all looking for a way to get rid of their curse, and thieves guild and DB would make significant impact only if you were discovered as a member in public at some point, otherwise both guilds are more or less subtle about their actions and members do not exactly post their pictures in the taverns, looking for women with "high position in dark brotherhood = situated and suitable father". So when joining the companions it's not like they'll know about it. Also, Companions are not "proud nords", they even have a dunmer in the guild. They are basically honored mercs, they don't seem to care if you're using weapons or fireballs to kill stuff whatsoever.
I roleplayed one of my characters by adding the cliche of amnesia, he was attacked and left for dead in an unknown country. Thieves guild were the only one who wanted him in and out of fear of lonelyness, paranoia and whatnot he joined. Doing dirty work for them he fell lower and lower and eventually started killing for profit which brought him to the DB. However, after he got his family in Riften killed by herd of vampires he started questioning himself and his ways and decided to turn over the page, joined the Companions after hearing about them using their fighting skills in a good way, and as he had the skills he thought it might be good idea to start doing good things there. Then he heard about the Dawnguard and having some history including vampires, and being immune to vampirism he didn't think twice.
Since at this point he was already well into the Nord culture and most of his close friends were nords he didn't feel like he owed anything to Imperials and when war started he joined the Stormcloaks along with many of his best friends, and in the middle of the war, on one of the raids in Helgen he became the Dragonborn.
College of Winterhold was joined somewhere in between Dawnguard quests, my character was looking to improve his fire spells to aid him in vampire cleaning and was directed there.
This way of playing actually requires a high dose of roleplaying considering the fact that the game itself doesn't provide the means to actually have "close friends" and whatnot, so creativity and past of playing lots of D&D sessions helped a lot in filling my character and his time spent in Skyrim with all the bits and details, instead of feeling like it's not right because I played a tabletop game.
As much as people hate on it, there's nothing wrong about roleplaying a jack of all trades. As long as it's not totally over the top (like roleplaying a dragon shepherd) roleplaying can help a long way in explaining stuff.