The reality is Jeremy and a good number of his top team simply don't have the brain power or wherewithal to reorganise it.
In fairness to them, they are far, FAR from unique in that sense.
I'm a historian by training, and the number of well meaning people who have tried to sweep out the stables, rebuild the stables, and decide to stable zebras not horses after all is by far the majority case.
It's especially striking when you look at say, post-Nazi Germany (lazy, I know, but the sources are the most extensive). It's all very good saying we'll prosecute and identify everyone who was a member of the Nazi party, but then you still need people to run the trains, the hospitals etc.
One thing that's incredibly striking is to look at the massive list of administrative functionaries. Some of whom committed suicide, fearing reprisal and punishment for what were relatively minor functions of the holocaust regime (no decision making or personal acts of murder). And others? Slap on the wrist, or demotion, etc etc.
Because they needed to keep the country running, and put the pieces back together.
Because it is insanely complicated to unravel even the most apparently straightforward of systems that society operates under. You can mostly just hope to gradually bring in the right faces.