It's an MMO, I'm sure quests will give you EXP.
The reason many games give you xp for quests is to incentivize powerlevelers to actually play through the story instead of just mindlessly killing the same mobs over and over.
However, I don't think it's obvious that ESO will go that route. Since a powerleveler may not WANT to play through the story, why not let them do their own (tedious) thing? Not written in stone that ESO will make that choice. In any case, seems completing some questlines will be necessary to unlock the next area, so that may be enough of an incentive.
MMOs don't all do everything exactly the same
Exactly, why force a player to do quests over mob killing, if the story is worth it, players will want to do it. However most quests are boring unoriginal time sinks, and even when forced to accept for XP, its just button clicking not reading so i can get back to the killing.
I see no logic in that. They seem to be following the skill usage system in order for the player to level up, the last time I looked. I would be somewhat illogical that you level those skills up by completing quests unless the quest giver gives you some training as a thank you.
In games where you have a limited amount of experience given such as Vampire: The Masquerade - Bloodlines there is somewhat of a push for you to do every single quest in order to become as proficient as possible, as a result there deters the player from turning down the quest giver regardless of whether they like them, wanna play a rebellious character which pretty much gives people the middle finger if when they talk down to you? You can do that, but you'll be at a disadvantage the more you progress through the game with that type of characteristic.