That approach to the situation (the 'Koeman isn't an Everton man but he gets the job done') is only reasonable if you were talking about a man with a glittering cv of going to clubs and being consistently successful. The truth is that Koeman has a pretty undistinguished managerial career, so it's not a case of holding your nose and going with him because he's a winner.
And on your other point of his inconsistency of performance: we cant afford (literally) to employ someone who'll give us such undulating contours to a season. We need incremental development at this club, not a snakes and ladders type of manager who'll drive us mad with month(s) long down turns.
I think both of those are good points. On your first there is obviously a relativity here. We have gone from
Moyes and Martinez who though each in their own way felt more natural Everton fits neither could be described as winners. There will obviously be people who will wan to downplay his league title wins in Holland, but he's won cups in Spain and Portugal as well. He's not Mourinho but relative to where we currently are he is a long way in his outlook from what we've had from the club over the last 15 years or so.
I haven't studied his time pre Southampton as closely, it's not so much game to game inconsistency as it is there are patches he does well. Whether we accept that or not is one thing but I can't say I am massively surprised at our form given the fixtures we've had and his past history in the PL. That's not to excuse it, but just as at the start when we were winning I urged caution, now I'd urge a little patience.
Evertonians want as you said a developmental manager. It's what
Moyes tried to do and it's what Martinez was trying to do. It was also all we could be under Kenwright. I'm not sure that's what Moshiri wants though. In that context I think the best we can hope is he is more Joe Royle than Walter Smith.