I feel like some of the criticism of Southgate is over the top and that he actually deserves a fair bit of respect for what he's achieved in terms of placings and how he's managed the intense levels of scrutiny that come with his job. He's clearly a relatable and intelligent coach who has the backing of the players, which is no mean feat in itself. But a lot of the criticism misses a very salient point...
International football is a completely different ball game to club football. The nature of the competition, and the eclectic composition of the side, dictates that tactics will naturally be more conservative, such as those Southgate uses. You can't expect players who don't ordinarily play alongside each other to gel, so the style of play will naturally be more pragmatic. That is what you see with England. There's no frills because the manager recognizes that imposing a freewheeling style of play is not feasible within a limited timeframe, and with players who are most likely frazzled from their club campaigns. The more coaches meddle and try to innovate, the more likely it is they will fail.
Pretty much any side that has been successful in international football has played a cagey style of football. Italy have achieved so much internationally simply because a cautious style of play naturally suits them. Spain were also successful playing boring football, ditto Argentina.