This is spot-on. Watching the game last night it seemed obvious that the biggest issue was no one was linking the defence to the midfield/attack. The defenders had lots of possession but no one in midfield was making themselves available. Rice was the problem because he can't take the ball under pressure and make quick decisions to release it. City had similar problems when Rodri was injured and that's why Phillips flopped as his potential back-up.
Exactly as you and Supercity88 say, the midfield is the crux of the problem as far as Southgate's squad utilisation is concerned.
There is a litany of problems that has been facing England ever since this competition began, from Southgate not arriving in Germany with the system and players properly sorted and ready to go; to his choice of players (eg no Grealish as an option, or at least as one of four wide players Southgate could have used to vary things in every game); to 'square pegs in round holes' (see Foden and Bellingham especially); to dealing with players' egoes (see Kane and Bellingham especially); and so on and so on as many others on here have pointed out.
But last night I was ranting and foaming (not a good look, I'll admit!) every time Jordan or Stones or Walker or Guehi or Trippier were on the ball, looking for forward passing options. Time after time there came none.
The whole midfield was stretched at least ten metres further away than it should have been, making links with the back four nigh on impossible and increasing the risk of the back line making errors under pressure from the (highly organised) Slovak team.
The individuals (especially the midfield group) on the pitch have to take some responsibility for what has happened during the four matches we've played so far (and Foden is included in this critique)
But given the numerous errors Southgate has made pre- and during the Euros, it is little wonder that we've been as bobbins as we have, even against, may I say, the 'less elite' nations.
I hope we can turn things around but I think it will require the senior members of the team to lead a squad session involving a long, hard look at what they are all doing and the direction they need to take from here on in, exactly as the 86 World Cup squad had to do with the floundering Bobby Robson.
Fingers crossed, who knows..?!