No idea. There is no guarantees at the top of any industry as to who will be the best. You can only see patterns and attributes that help someone reach the top of their field. Application, attention to detail, being intelligent, working under the right people as they learn, having experience that is useful to the future direction of the space.
Its a rare individual that has all these attributes and can get other people on board with their vision. The fact its such a hard job means that plucking random players who had decent playing careers and expecting them to magically make top managers is frankly bizarre. No other industry does this. You wouldn't say to someone who worked stacking shelves at Tesco "right, we are going to send you on a years management course and then you are going to run Tesco UK at the end of it".
The reason former players get offered the job is because they easily have one part of being a good manager down without much trouble. Having the charisma to led the fans. Good managers needed to not just get the players on their side, but the fans as well. Managers that loses the fans will quickly lose the players. It's why people like Moyes failed at United. No matter how decent of a manager he was, he utterly failed to convince the fans adequately, and as a result imploded at United.
Popular players have the legacy with their fanbase that they can at the least ride out a few bad games. Ole lasted so long as United manager was all because he is considered as a legend at the club. On the other hand, it is hard for fans to buy into certain managers if they don't have a well-known playing pedigree. That will affect the players and the results.
The technique was never the problem, their playing style and useless managers incapable of coming up with a cohesive lineup and balanced approach to the game was much more of a "perfect example" of why England failed. But you're coming up with some highly subjective opinions and presenting them as absolute facts across the board, so this is pretty useless.
I'll argue it's not a question of technique, but
positioning that made them flatter at national level.
What is the thing Lampard and Gerrad have in common? They were often used as CAM because they were not positionally disciplined to play a deeper role. England have no real issues with attacking players, or even attacking midfielders. England have a big problem with
defensive midfielders.
Makélélé had an entire role named after him because prior to his arrival at Chelsea and in the PL, England simply do not have that many players being able of playing his role. Yes, you have plenty of tough "midfield" generals. But even them like Roy Keane (I know he's not English, but he came up from the English system) are box-to-box players rather than a real deep-lying midifielder.
How many English Deep-lying midfielders do you even find? You have Carrick and that's about it. On the other hand in other major footballing countries, you have a wider number of players who are top-level in that position. Even today, England lacks so many top players in that particular role that they had to give that position to a player who formerly spent most of his years in the championship (Kalvin Philips). And Philips isn't in any of the big 6 clubs. All the top Deep-lying midfielders at the top 6 clubs all come from foreign countries.
Even a youth player from Barca trained in that position lost all positional discipline after spending years in the PL. (Fabregas).
The problem was with the rise of Pep Guardiola and the ushering in of Spanish and modern German football, they have managed to enshrine positional play football as the most dominant system of tactic there is. But all those coaches still needed to recruit non-English players in that deep midfield role because England simply aren't producing those positionally disciplined players.
England is behind on positional play, and still is to this day. Pep and Klopp dominated the PL because many other their rivals simply can't cope with that. Burnley the most "traditional" English team in the PL, regularly gets completely destroyed by Man City because they can't cope with positional play even when they park the bus.
But yes, we aren't speaking of ultimate truths, personal preferences matter obviously.