This paragraph in Stephen Bush's mailout is pretty on point - and highlights why Labour were always keen to avoid an independent overseer in the first place...
It highlights the political difficulty that the move towards an independent process will have: on the one hand, Keir Starmer needs to demonstrate that change has happened, that his actions match his words and that his promise of 'new leadership' is not just a slogan. On the other hand, the biggest single promise of 'new leadership' is in giving away power and handing the complaints process to an independent overseer. The Campaign Against Antisemitism has already announced that it is submitting complaints against 14 sitting Labour MPs and you would expect that when the new process is in place other organisations will do the same. What happens if an independent process concludes that on the balance of probabilities, some of the 14 MPs should be expelled and some should not? What if the ones to be expelled don't 'seem' to most observers to be the most egregious offenders?