Whilst what you say has merit, and does carry weight at the highest levels of competition, the most fundamentally important thing a team typically needs is a midfield that can control and dictate the tempo of a game, be that to speed up the play, slow it down or drain the optimism out of the opposition, which leads to the enthusiasm in the press dissipating. That in turn allows your own side to start being more expansive and probing with their passing - taking risks that don't compromise the shape of the team nor allow the opposition the opportunity to counter at pace.
England need to sort out those fundamentals before worrying about expansive passes and probing because that's no good if every time you lose the ball, the collective take an age to win it back and also have little time resting in possession when they do. That leads to exhaustion and considerably diminished performance levels in the second half of games as well as panic and terrible decision making once the concentration levels assuredly drop.
You don't have to control the game via possession, but if that's not your route, you have to be oppressive in another manner with a midfield that is specialised and capable of facilitating whatever the attack needs - think of Klopp and his unspectacular midfield doing the grunt work to allow Mane Firminho and Salah as well as TAA and Robertson all that they needed to constantly work over the opposition. But of course, Southgate is a donkey, so there's no point to considering him competent enough to set up a midfield to deliver with a focus on uniformity.
England don't have the midfield unit to play highly intricate technical football, but they most certainly have the personnel to dictate tempo and better control game management into the second halves of games, and the better you can do that, the less reliance there is on a maestro who can bypass the more perfunctory with a single, penetrative pass.
If you're looking for a Scholes/Xavi/Pirlo/Kroos etc. level passer, England don't have one of those, but teams like Klopp's have shown you don't need one if you know what you are doing and can execute it to the letter as a unit. The only reason this side resorts to amateurish hoofball in second halves of games is their manager and his inability to instruct or instill calm. Not one of the players in midfield come from hoofball at club level, so it should be no surprise they are extraordinarily shit at it as it's alien to them. Wharton or Mainoo in there, with a coach that encourages constructive build up through the midfield, and the side wouldn't look half as bad as Southgate makes it look.