The 3 best coaches in the EPL are directly or indirectly influenced by the total football concepts of the 1970s. Klopp in his own words implemented many of Arrigo Sacchi's ideas into his thinking and Sacchi in-turn was influenced by Rinus Michel's and the Dutch total football concept.
Erik ten Hag isn't wedded to the total football concept and has implemented ideas into his team from other cultures. The only similarity between LVG and ten Hag is that they both follow the positional play principles. But LVG was risk averse in comparison to ten Hag, who not only looks to implement a high risk vertical style in possession but does that with a view to playing the game in the opponents half in a compact high block, along with creating conditions to implement controlled chaos off the ball.(counter pressure off the ball). That's a big difference to the LVG we saw at United.
I do agree with you that it could take longer for ten Hag to implement his ideas compared to Poch. Ten Hag's ideas both in offensive and defensive transitions are of a higher level in comparison. But teaching that type of football could take longer to implement, but if he gets it right, then the football is gonna be devastating.
Arrigo Sacchi once said in a interview, 'that I haven't arrived at Milan to conform to the Italian reality of playing defensive football, but I've arrived to attack that mindset'. And he did just that by implementing a brand of football that would influence a generation of coaches, similar to how he was influenced by Rinus Michels. I feel we should adopt that mentality.