I'm among those frustrated by the 'lack of playing identity' but is there a pattern to the madness?
2012/13: Possession until after Sturridge/Coutinho arrive, where we moved towards counter attack. When Suarez was banned, we played counter attack. No high pressing, we dropped off and pressured in our own half all season.
2013/14: Possession until near Christmas when the diamond and Gerrard-Pirlo took the league by storm. High pressure (not really pressing) and lightning quick transition to attack.
2014/15: Possession until after the new year when we moved to the 343. Then using high pressure and trying to move the ball at a high tempo into attack, though not as swashbuckling as the diamond.
Possession in the start of seasons, moving towards a higher tempo, high pressure, counter attacking (but still playing football) football for the second half of the season.
Combine his periodization training... it looks like Rodgers ideal is to use possession football to control the pace of games while the team is still getting fit, then transition into a more aggressive football later in the season. Only problem is, we've not been any good at playing the slow-tempo possession football, ever!
Anyway, this leads me to my comment on the thread's topic: are we never after world-class DM because we aren't looking to play the slow-tempo possession football for more than a few months of the season, before moving into a high press/pressure system when fit? In the latter system Lucas, or a Busquets or Martinez, wouldn't fit in as well with what Rodgers wants to do, would they? Although it still raises the question of why Lucas wasn't used in the start of the season...