To some extent, leveling a character much past 30 or 40 almost requires doing all the factions. Not to mention being able to visit all the areas that are quest locked to factions.
Not true at all. I gain more experience walking to my quest targets than the quests themselves. Hell, I get more experience hunting. Now if all you do is fast-travel, then yea, you may have a point.
Go hunt deer in the Rift with Runes and see what your Destruction skill does.
Seeing as all experience comes from skill usage, and none comes from actual quests, it is possible to level without ever doing a single quest.
So I guess my comment was more tied to trying to level a well defined (e.g. uses only a handful of specific skills) and non-exploiting (e.g. not spamming muffle to level Illusion) character.
My level 50ish character has completed Dawnguard, Dragonborn, Civil War, and the main quest line along with miscellaneous side quests for various holds.
Even so, without resetting a skill to legendary it is very hard to level, no matter how many deer or vampires or dragur are killed.
Mostly this is because my primary combat skill is already 100 and things like speech and lockpicking level very slowly.
Without leveling skills I never use and which are not part of my character, like magic schools, I'm left to level very slowly.
Thus for me I either start doing the various factions simple to break up the monotony, or I shelve the character and start all over.
At this rate, I'm not sure I'll ever see the Ebony Warrior without making some generic character that uses every single ability just to gain levels.