There aren't many english players at the top of the game, nor managers, because british/english people have a attitude problem. When the rest of the world changes, we don't, because we invented the sport so we know best. It's ignorance and english football is falling behind at a pace that is gathering momentum. It was just Spain, then it was Germany, now it's Belgium and half the countries in between. They've all modernised both training of players and coaches/managers. England refuses point blank to do so and as such we'll suffer a lack of managers except those who get trained, unsurprisingly, by foreign managers/coaches.
No surprise with Rodgers as he has had a huge influence from coaching under other foreign managers and frankly from taking over a team that was already managed by someone who was teaching passing attacking football. It's very hard to take over a Stoke or Sheffield Utd with the players they would have had and ask them to play passing football. In general you're kind of stuck playing whatever works best for the team, it's lucky he could take over teams capable of playing the "right" way and not getting stuck in a rut of crap football.
Really the simple part is, coaching, as with teaching it's a numbers game. No surprise that in education classes that are say 5 or 10 to 1 teacher do better than classes that are 20 or 30 to 1 teacher. No different to coaching. Spain has more coaches. It was 3 years ago now but Spain had 24k coaches at Uefa b/a/pro level of training, England had under 2800. Now work out how many kids are being taught by top coaches in England vs Spain?
There is SO much wrong with the way England tries to teach it's kids football..... not surprisingly this leads to less great english players and English managers/coaches are largely behind this.
Every single premiership club could offer free training for coaches at grass roots teams and pay what is literally, or say ask 500 people to sign up for it every year. Pay for them to become coaches and assign them to youth teams to get more people involve with proper training at every level.
England just won't do it properly, and they won't accept they are doing it wrong, it's embarrassing. WE need English managers to both go and do their coaching badges abroad(very very few do, again attitude), try and get jobs under better managers, and attempt to get jobs at foreign teams.
A guy who is assistant manager under Pardew or Redknapp, or players who pick up management from the managers they had in their careers, aren't going to turn into the best managers themselves.