Caporegime
You need to join the dots here - there's a reason why the only managers you can attract are generally ex players. Top class managers won't touch that job - when they tried it with Scolari 20 years, he made it clear why he wasn't interested.
There are very few top class managers that are in high demand that take international jobs. They are usually taken by older managers who have had their careers or by second tier managers.
France - Deschamps
Portugal - Martinez who seems to like an easy life and has moved from underachieving with Belgium to kowtowing to Ronaldo at Portugal
Germany - One of very few teams to have a genuine desirable top class manager in Nagelsmann
Belgium - Tadesco
Brazil - Dorival Junior
Argentina - Scaloni
Italy - Spalletti, a good manager to be fair
Netherlands - Koeman
Spain - Luis de la Fuente
How many of those would be getting jobs at any of the top domestic clubs in the world. 2 or perhaps 3 out of 9 if you are being generous. We could very much have a better manager than Southgate very easily however. Thats ignoring the fact that I think a dead possum wouldn't be much of a downgrade on Southgate.