I don't even think the manager needs to be that good really, there's plenty of non top level managers who win things at this level. They need to be half decent tactically and fairly sound, while also managing to be a bit lucky. While it sounds mad citing luck as a thing, you can spawn your way to a World Cup/Euros cos the format is so short. He seems to manage the fairly sound bit, he's had the luck you need, but he definitely hasn't got the tactical bit.
There's some very average to poor managers who I think would give England a better chance than Southgate, including the man he replaced.