There's a great deal of laudable sentiment in what you eloquently express here.
The wish to achieve and see fulfilment of dreams is admirable, if a tad utopian, but I admire and don't disagree with the sentiment.
Wigan winning the cup was their Andy Warhol, '15 minutes of fame' moment and honestly, I doubt anyone would genuinely deny them that and the immense pleasure it gave their fan base, together with so many others who watched a David overcome a Goliath.
Where this relates to Everyon as I see it is... El Bob did well to win that cup, but at the expense of relegation. He inherited a decent Everton side and added Lukaku, and (up until the crushing defeat at the pit) had rekindled great hopes within many, many Evertonians.
Sadly, regrettably, lamentably, he was not right for a job of the magnitude of Everton and his shortcomings were cruelly exposed and he was unable to adjust anything remotely like sufficiently. His third campaign merely served to confirm that he was out of his depth and despite reaching two cup semi-finals, the club, fan-base, media and Insuspect deep down he himself knew he was done.
His departure was the best for all parties. He moved on to a job that he is better suited to in my opinion, and we moved on with a more pragmatic if somewhat tougher approach under Ronald Koeman.
I bear El Bob no real malice but, I sure that Everton will be better and have a far greater chance of trophy success under Koeman.