Moyes has been been the most 'successful' (without ever winning anything) manager in my time supporting Everton. Brought stability when we needed it, put together our best squad in recent years on a shoestring and made us a fixture in the upper echelons of the table. He did a lot of good for us and I shudder to think where we'd have been without him.
His game plan was effective - if a little stodgy at times - but built around the unit. It's clear to me how much Lukaku, and perhaps to a lesser extent Barkley, papered over the cracks of the Martinez and Koeman philosophies. Most things will look good if you have a 20-goal-a-season striker knocking them in, but we saw on Lukaku's quiet days the frailty of the systems.
And now we're paying the price for failing to bring in either a target man and/or any kind of pace option (and a reluctance to use those we do have).
All this said, however, Moyes lost a lot of respect with the 'get out alive' and 'holding back their careers' comments. No-one could really begrudge him his move to United, but his attitude after left a lot to be desired.
Plus, I think the game has moved on from his style a little bit. Perhaps it's harsh to judge him on his time at United, Real Sociedad and Sunderland (enormous, unrealistic expectations after Ferguson - completely different league, obviously a duck out of water - sinking ship, which ambitious players would want to join Sunderland?). But I don't think the 4-1-4-1 formation is currently used to great effect any more in the PL.
I still think he could do a job at a well-run, mid-table club and improve their fortunes. To many outsiders, that is what Everton are at the moment, and given his affiliation in the past, it's not an unreasonable shout. I'd probably take him over Koeman right now. But I think most of us would agree it'd be a massive backwards step and there are other options we'd be better off pursuing.