There is no doubting or disputing the job Southgate did in rebuilding from a pretty dark place, towards the end of Capello, through Hodgson years, and let's not forget the Allardyce incident! Southgate has brought us lightyears ahead of that and that holds my respect.
My concern is whether he can make full use of the quality and potential now at our disposal, when it comes to the sharp end of competitions when we meet nations with equal or more quality. When I think back on the Croatia, Italy and France games, they all could have been handled better.
It's a small sample size I know which contributes to the pressure on those occasions, and you make a fair point that a slice of luck comes into those games.
I'm also aware the next question on my trail of thought would be 'who would do better' as with any debate over a manager. Beyond my bias for Eddie, I'm not exactly flush with names. Potter seems to get a lot of media praise but I'm not bought into it yet. Mourinho would be the antithesis of Southgate's man management.
One specific nitpick, I also don't get Southgate's ongoing aversion to picking Fikayo Tomori given we need CBs and he starts every week for Milan consistently in the top 4 of Serie A (currently 2nd).