The CoC simply does not work with regard to welfare issues, and will never work again in the way it did in the past. The days of the CO of a unit "enjoying" paternal responsibility for almost all functions of his unit are long gone. Housing, for example, is now the responsibility of a faceless executive agency and the powers of the CO to effect changes are limited.
Budgets come down from on high with associated targets and there is simply not enough to go round, even for essentials.
Pensions have been changed to the disbenefit of the majority. There was a sham "consultation" carried out with leaflets being distributed on an approximate scale of 1 per unit!
Voting arrangements were changed with little thought as to their impact. It took a grassroots campaign to restore these.
There are other issues as well (continual breaching of tour interval thresholds, etc) and the CoC cannot represent the interests of the soldier, sailor or airman. Many bad decisions have been made at the political level, and there is no means of influencing this process - the Commons Defence Committee often has its concerns dismissed by the MoD.
BAFF is necessary if serving personnel wish such representation, and the indications are that they do. MoD are vehemently opposed to the organisation as it will undermine the ability of MoD to simultaneously cut everything to the bone and spin the "everything is OK" message.
Finally, there are no provisions in QRs or the single-Service Acts to prohibit such an organisation, or membership thereof. BAFF is happening.