Not sure about the England shout (although maybe, as there's been some tosh who've had the odd game for that lot). But the examples you give above: Livermore and Davis are apt...that sort deserve a place in a starting line up at middle ranking clubs for sure. Henderson is different as he has a dig on him and can get a few goals, so that elevates him above the decent but unspectacular midfielders.
I'm not running Davies down. He can do exactly what he says he must do (improve all the core skills you mention above) and be a starter for Everton for years. But he must progress and develop his game from this point because, IMO, it wont be enough as is to command a starting place in a team that makes a tilt for a top four spot.