The issue with those stats are Cooks win ratio is bosted by League of Ireland, L2 and L1 campaings while Monk and Hughtons are dragged down by Prem campaigns. The best comparison is just doing Championship only where the difference in quality is mouch more telling.
Gary Monk
Games - 126
Wins - 51
Draws - 34
Loses - 41
Points per game - 1.48
Win Ratio - 41%
Chris Hughton
Games - 206
Wins - 108
Draws - 60
Loses - 38
Points per game - 1.86
Win Ratio - 52%
Gary Rowett
Games - 180
Wins - 71
Draws - 61
Loses - 48
Points per game - 1.52
Win Ratio - 52%
Paul Cook
Games - 50
Wins - 14
Draws - 13
Loses - 23
Points per game - 1.10
Win Ratio - 28%
Cook is the only one who lost more than he won and only just has 1 win more than he drew, while the others have won healthier win to draw ratios. Also worth considering that out of Cooks 14 wins, 5 of them came in the first 10 games of last season when we were riding the motmentum from promotion, once that momentum stalled it's 9 wins from the last 40 league games and dropping to a win ratio of less than 25% which is lower than Joyce.
Even if you take out the better clubs and focus just on teams fighting relegation battles - Rowett, Monk and Hughton all took over relegation clubs at this level and they all out performed Cook and turned the relegation battlers they inherited into promotion challengers the following season and after this summers spending spree probably didn't spend much more, if not less money doing it.
If people think Cook will turn it around that's a case of judgement but the 3 managers mentioned are better than Cook at this level. For me if we could get Hughton or Monk it's absolutely a no brainer that you sack Cook and get them in - they would be significant steps up - just like Cook was a significant step up on Caldwell, Barrow, Malky, Joyce, etc. I believe Cooks has taken us as far as he can and we need to trade up for someone who can take us further if we want to do what IEC need. I'm grateful for his efforts to get us to the point we are at now, but just like Pulis, Allerdyce, Bruce, Warnock, etc all have their limitations - they are brilliant at taking you to their ceiling but then aren't capable of taking any team beyond that (eg promoted but cant keep you up, or prem survival but cant ever push into top half, etc) i think Cooks ceiling is relegation battles in the Championship from what we've seen over the past 50 games and i think we've got a squad capable of mid table mediocrity at least.