The reality is though "better than Martinez" is not our only benchmark. Currently there are probably 18 managers in the PL who are better than Martinez. Moyes is better than him.
The key point in this, is to note the change at board level. Had Moshiri been around 3 years ago I doubt we'd have got Martinez. So I take it as red that we should be attracting a manager better than him. I think what we would like to see this summer is a real statement of intent. Of course Swansea & Stoke wouldn't say no to Koeman but again that does slightly miss the point, that we are trying to make a statement and as a fanbase begin to accept the idea we are bigger than Stoke and West Brom.
For a lot of fans that means mocking the above teams, or talking about our great history. However to really be a big club we do have to start thinking how a big clubs fans do, and that means having targets that go beyond "is he better than Wigan's ex manager" or "is he good enough for Stoke, Swansea or West Brom". Fans can't have it both ways. Complain about irrelevance in the eyes of the media, but in their own minds lump us in with those clubs.
As it happens I am not that anti-Koeman. None of the above necessarily discounts him but I do think as fans we need to shift our arguments somewhat. To be fair to Moshiri it could be that he is after better managers and they have turned us down. In all fairness to him if that's the case there is not an awful lot he can do. I would rather we tried to Mourinho and got knocked back than not bothering.
Remember City's first appointment was Mark Hughes. They then went to Mancini and Pellegrini before eventually getting the very best. Mourinho being available for us may have distorted the market a little. Normally we would have no chance of him, but circumstances have given us a glimmer of hope.
As for Koeman I think his work at Southampton has been very good. I think he'd be an ok fit for us. he has worked with a similar squad to ours and outperformed us while having to rebuild. He has shown some ability to bring players through. His record abroad is hit and miss, some successes and some failures. He is a big name player and will probably help us in bigger games. On the downside managing Southampton is a long way away from managing where Everton want to be. He is a steady choice but the rewards are not as great as Mourinho, or indeed the next rung down of De Boer, Emery or Tuchel.
I can only hope, if we get Koeman that it is alongside a change in approach that sees Everton managers having a job for life. If we progress how we ought to progress, with the sort of funding he may have Koeman to date hasn't shown me too much to show he can be a top manager. All we can hope, is if he stabilises us similar to how Moyes did and hits a ceiling that we would move him on and "upgrade" similar to how Citry have done.
The only final point I would make would be, in the eyes of the media and the wider world it would be a big statement. For us to take Southamptons manager would indicate a level of ambition that we haven't seen for 20 years. Taking a side who finished above us twice and are in the top 8 is something we haven't done in 2 decades. That does give me some confidence.
Esk has indicated there have been talks with more than 1 manager. It may be he comes across best. He's not my number 1 choice and I would be underwhelmed but not dejected with him. I think he will do a solid job but do worry we'd hit a ceiling and can only hope if that happens he will be moved on.