I don't think it's about trust personally. I just think when Barkley plays in the 10 position. He doesn't run past rom enough.
Davies seems to make more positive runs. Maybe this is what RK wants from that centre position. Sigurdsson or maybe Klassen who we have been linked with, could be set for that role next season
Totally agree with you there mate and your bang on the button about Barkley not making enough runs past Lukaku from deep. Plus, he takes too many touches of the ball in midfield does Barkley and Koeman as already said he doesn't want Barkley in a deeper role, in his own half taking too many touches than necessary and risking losing the ball in dangerous areas. So I personally don't think he trusts him in there and that's why he's shifted him out wide as part of the front 3.
But Koeman prefers a 4-3-3 system and will want a more forward thinking, creative CM in there that will add goals and someone like Sigurdsson, or even Klaassen like you mention, would be ideal. Davies is in there atm, and rightly so, and he's been trying to make those late runs and get in the box but atm I don't see him as a type of player that will get us double figures in goals and assists from that position just yet. He may well turn out that kind of player but atm I see a similar kind as Gueye who will put himself about the pitch and Harry and harass players, Nick the ball and get us going, then obviously you've got Schneiderlin as the sitter, one who screens, wins ball and gets us going. We just lack that creative player who gets goals and links midfield to attack. I'm sure we all thought Barkley would be that player but I don't think Koeman sees it that way or else he wouldn't be pushing Ross wide to accommodate Davies being in the centre?!