With regards to why our players seem to play much better after they left. I think the answer is very simple.
Liverpool do not play in a certain style. Yup.... All teams can be successful to a certain extent by adapting the players to play in a certain style.
Arsenal plays a quick one touch passing by passing the ball into the goal, literally.
Chelsea builts their team based on teamwork and defense and scrappy 1-goal wins.
Totteham become successful by playing and passing the ball well...
Liverpool... really not sure we are good in or what we are bad in.
I guess the only time we are successful in recent years is when Gerrard Houllier played a counter-attacking game which won us 5 trophies... 5... even the old liverpool teams may not win 5 tropies in one year (over 2 seasons).
Under criticism, Houllier change tactics and played offensive but never regain the form.
I think a lot of time, players and fans alike, were confused by his strategy and substitutions. Rafa at least is being more consistent by replacing a DM with DM (Diao for Hamann), RM for RM (Nunez for Alonso) etc...
When the players are confused, esp like Kewell (he played as RM, LM, CM, Stiker), they just can't perform their best.
Simply as that. Sad but true.