Independent of whom ? Which cases should he intervene in and which cases should he not interfere with ?
Which cases should be dealt with immediately and which cases should have due process ?
I'm asking this because it seems you're all over the place on this subject.
All cases should have due process. I'm not in favour of the idea being mooted of automatic expulsion on referral. Cases need to be 'triaged' quickly to determine if a case is serious enough to warrant immediate suspension while investigated (does the behaviour have an immediate, ongoing impact on the ability of others to engage and contribute?). There needs to be clear target timelines for all cases, not just the high profile ones. There needs to be a process for malicious or over-sensitive referrals, too.
Independent of... any perception of political interference. Any disciplinary body which is exposed to (or perceived to be exposed to) several types of potential compromise to it's independence is no longer fit for purpose - and it's worth recognising that that purpose now is not only to deal fairly with accusations of antisemitism, but
to be seen to be doing so. That means if the body's leadership or staff is subject to appointment from any other part of the party; or if it's decision making process is subject to arbitrary review by other parts of the party (and yes, I'd include Tom Watson in that).
For the Labour Party currently, that is a problem. Clearly it has to be independent from the leadership - but also right now that needs to extend to independent of bodies accountable to the membership, given clear concerns that the problem stems from the 'new membership' of the party, or at least it's most vocal elements and representatives.
I also recognise there's a bit of hypocrisy from some critics of the leadership on this subject, demanding the leadership crack down on antisemitism, yet also that the leadership does not interfere in the process. That leaves quite a narrow scope for the leadership to provide 'acceptable' focus and urgency. It must be said though that the clearest way to provide that leadership would be to be much clearer about what is unacceptable; and it can't easily do that, because certain elements of the leadership clearly don't get it. A quick glance at any twitter discussion on the subject reveals that there are plenty on the left who simply don't recognise that asking "who is Tom Watson working for?" alongside a list of campaign funding from FoI and a Jewish philanthropist is wrong. It needs to be spelled out by the leadership that being a 'Friend of Israel' - even, a self-proclaimed Zionist - is actually okay within the party. People don't have to agree with the view, but it has to be made clear that the Labour Party is not, and can not become, an organisation dominated by a single ideological purity on the question of Palestine.
So, it's going to have to be independent of the party itself - or a wholly reconstituted body within the party with structure, accountability and remit designed based on independent recommendation - and some degree of auditing - from outside the party. Perhaps something accountable to 'trustees' from within and without the party which do not and cannot be seen to represent - or be immediately reactively accountable to - any particular strand of party opinion.
An institutionally racist organisation cannot fix itself alone. An organisation which believes it is wrongly perceived as institutionally racist should be desperate for independent confirmation.
