Been thinking about our league form recently and how Carlo is changing the team slowly. We seem able to cope(almost) with top table opposition but unable to break down lesser teams unless we are away from home when we seem to do well against all comers. My theory here is that Carlo plays a very defensive game against both top 6 teams and in away games with a focus on the fast break to score, this would be supported by the number of 0-1 wins this season (I'm sure one of our statto's can check if its more than usual against Top 6 and away games only). The above style requires players to be disciplined and defend well which is ingrained into almost all of our players (James, Iwobi, Siggurdson excepted)
So why the issues against weaker teams at Goodison? well my thought would be that its here that Carlo changes to a ball carrying team which uses passing to break the lines of a higher press, and this is something the players are trying to learn as they have not been used to it in the past. Our CB's do ok carrying the ball out of defence but clearly either the short pass to midfield or the accurate long ball is not a natural skill. They get the ball back from the midfielder a lot. Keane at the start of the season was doing well with this but has done it less with Godfrey next to him (not sure why). When the players cannot or do not execute this well, it results in us losing the ball to either the front line opposition or more likely in midfield which results in a forward break for the opponent with our midfield out of place (and pace). So Allan or Davies look like they are off the pace/play. You can see Napoli play like this under Carlo.
How can we get better at this - sign midfielders who see the spaces, turn quickly and have pace to move the ball forward. That is not Sigurdsson or Gomes. Doucoure and James can do it but both often find themselves pushed wide by the presence of Gomes/Siggurdson/Davies. Carlo has been trying to get Iwobi to do it but he also favours wider play AND more importantly does not have the vision to slice open/cross to Richy/DCL once he gets the ball. Siggurdson has that technique but not the speed to turn defence into attack. so we've seen Siggy create a couple of chances like that for Richy but Iwobi ends up running with the ball across the field hoping something opens up to his limited vision.
The answer is clearly new CM players in the summer and patience until then. Sorry for rambling, I know TLDR....
Much can be said about what you write, but for now I want to mention the following:
Godfrey has played for Norwich, and who under Farke is known for a ball-possessing style.
Digne former Barcelona and French national team player.
Mina formerly Barcelona, and plays on the Colombian national team.
Allan played the football of his life under Sarri.
Gomes formerly Valencia and Barcelona, and Portuguese national team player.
Iwobi has played under Wenger at Arsenal.
Gylfi has played in Swansea, which just has a ball-possessing philosophy, has among other things had Laudrup as coach.
The list goes on. But my point is that many of these players come from clubs, and have received their football education in clubs where you have to play the ball along the ground, break the lines, and look for space between the lines. Playing out of pressure, etc.
What must also be included in this equation is that Ancelotti has a fairly defensive philosophy, and is less concerned with having the ball than many other contemporary coaches.
Naples as you mention, played very good and entertaining football under Sarri, and became known for this. Under Ancelotti, they were nowhere near this level. Sacchi, Ancelotti's good friend, said that Ancelotti should not take the job in Naples, because he could not possibly recreate what Sarri did.
This was not because Ancelotti is a bad coach, on the contrary, but what Sarri did in Naples was so innovative, and Ancelotti does not have those ideas.
My hypothesis is that Ancelotti is simply doing what he thinks will give the best results now, with the players he has, and not thinking far ahead. He is a coach who has mostly coached the best clubs in Europe, and has not had time to develop the teams much. He has done what is safe, and which gives results. We humans get some psychological habits eventually, and that's what I think this is.