I don't think they necessarily need to remove the story quests, but they definitely need to remove the obligatory component to it - especially for old content. Keep the quests for people who want to do them, but don't make it a requirement to do them so as to unlock everything.

Suddenly, people can level at a pace they want, however they want - be it through quests, dungeons/trials, fates, etc - and they aren't locked out of new content like new jobs.