Sigh, we're here again
The reason you can't name a manager who has turned it around is because clubs don't wait to find out if they can, not that it can't be done. I'm sure pre PL there may be some examples when the game was less cut throat.
The great managers build teams then rebuild them, given what they need to do so when they need it. Wenger done that a couple of times & Fergie done it several times - i think both would have struggled to rebuild their teams if they didn't get investment at the right time and as we know due to financial constraints we couldn't give that backing - so the options were either fully invest in the managers vision and give him the time to rebuild post stadium move once money was there or to try and eek something more out of a squad & team that was clearly on the wane.
Of course we are here again because
- The argument is the club fired Poch too early
- Yet you admit there is really no data to show that if he was given time it would have worked/changed (so the premise is nothing but hope)
You Wenger example is also great, yes he rebuilt teams when at the top, but once it spiralled off he was never able to recover to anywhere close to his original achievement.
And for @Finney Is Back you are mixing up conversations
- Are there problems above manager that need to be addressed? are the decisions post Poch bad calls? -> yes
- Does that change if the decision re Poch was right/wrong? -> no, nothing to do with the above
Managers have a shelf life (there is lots of evidence of change being effective, very little that staying the course works), and how good they did at their peak doesn't change that