You're talking about individual players who play for clubs with foreign managers and surrounded by world class foreign talent. Take those individuals out and put them in an England team and it's a different story. England don't really have a blue print or style of play like the Dutch, Germans, Italians or French. It's not an accident that England haven't won a major tournament in 58 years with so many different managers - trying and failing. One could even argue 1966 was a fluke really, especially had VAR been around, where all 6 games were played at Wembley; like Euro 1996 and the last Euros all bar one game.
There's also the same problems in midfield that have plagued every England team I have watched - the English disease of giving the ball away is a recurrent theme; as well as Moving the ball quickly and accurately enough upfield and understanding how to create space and exploit it.
The premiership is a big impediment for the national team - with so many different styles of play and the division of ownership. The national team should be the pinnacle of the game in England, but it's not and club game is definitely top dog. That means clubs not prioritising English talent who are bought and sold at ridiculous sums. I think the stat is like 30% of players who play in the premiership are eligible to play for England, but not all of them are world class.
I have always thought Southgate will only get England so far. He's perfect for the FA. - being an FA man, good PR, no stories Ala Ericsson, Hoddle, Allardyce, he's also English after the failure of Ericsson and Capello. And won't rock the boat for the cash cow that is the Premiership.
As I said the issues are multifaceted and not all down to the manager.