Spot on.
And to underline your point further, the team has no more cohesion, tactical sophistication, or understanding than they did under Southgate. They may even have slightly less.
The conclusion I draw from this, personally, is not that Southgate is better than Tuchel necessarily, but that national teams just have the players they have. The guy in the dugout is not that important. Even if he is a genius, he has so little time and games with the players to affect their method of playing that it doesn't matter how clever he is.
This mad idea the FA have had for over 20 years that to spend enough on a manager with a big enough name and CV will make the difference, has once again been disproved. Didn't work with Sven, didn't work with Capello, hasn't worked with Tuchel.