The squad is great, and Southgate seems to be very uninspiring and mediocre.
But then, as
@Dante says, there's only so much time a NT manager has anyway.
Therefore, another problem I'd attest the English team apart from their manager is that they have no real block, of players from a top team that are used to playing together and might form some sort of spine.
The starters are from Everton, City, Chelsea, West Ham, Man United, Aston Villa, Leeds, and Spurs.
Only City have a block of three starters, but then these three are not really what you would call leadership players in terms of mentality and experience. And they're also not connected on the pitch.
It's a result, partly, of the PL's specific quality, with top players in many teams, and especially the English top players evenly distributed since most of the best players in the best teams are stars from abroad.
And it's ironic that circumstances have made it so that the most "English" top team of recent years, that could have served as a base for a team with a spine, and that is very well drilled - Liverpool - has no starter at all.
Trent, Henderson, Gomez are injured, Milner has grown too old.