I have something in my head for some time now but I'm not sure I can explain it properly in English so please forgive any mistake
I think is it due to lack of quality of players to play alongside Naby (and also Fabinho) that make Klopp struggle to ease him into games. I mean the like of Hendo, Gini or Milner themselves are not at the level to tolerate the mistakes if any made by new/younger teammate who trying to settle into the team. Please see the way Gomez adapt superbly into the team with world class partner such as VvD. Or when we have Suarez we can ease Sterling into the team to let him develop. Currently our midfielders no one even close to the level of VvD or Suarez so Klopp reluctant to introduce Naby or Fabinho into games that the result is really important.
It's like Klopp do not trust the old guards than he do not trust his new signings.
I think that is spot on, but I fing that odd, these aren't rookie players, they are all highly regarded international players. Klopp has to just take a chance on them, it might be one step back before you can move forwards but its certainly clear now that the future cannot be Henderson and Milner as a midfield duo.
Against Everton I would be tempted to play Milner purely for his physical presence but I'd play him together with Fabinho and Keita or perhaps Gini and Shaquiri. I would then over the next few weeks get to a position where our main midfield would be Fabinho, Keita/Gini and Shaquiri.