On the first point, yes having United on your CV is worth something however the job he did here puts a huge stain on it. It's not like us, where if we have a big name on our CV it means the world because largely your future employer has very little knowledge about the competence you showed in the job. For Moyes, his failure is public. They know although he was our manager, he also flopped. That will largely negate any positive he has from it. With regards to Everton, yes I agree there. The job he did here won't tarnish that but it will always pose the question on whether he can manage a big club, or take a good club on to being a big club.
To your second point about fan opinion, it does hold weight. Whilst it is just a factor in the selection process, fan opinion plays a role just like any stakeholder. A chairmen wouldn't want to hire a manager who would not satisfy the fans, because it creates problems, particularly of they fail. It could impact their credibility and so the risk of hiring a manager who has just come off such a big humiliation is more risky than other managers who aren't so high profile in terms of ther failings.