But ID is not a 'travel document' for domestic travel.

Perhaps it would be advisable to be somewhat circumspect before assuming that others are clueless and are "vaguely throwing words" and that only you is aware of the relevant requirements. Since you seem to be so familiar with the legislation, it will no doubt not have escaped you that transparency is an important factor in the evaluation of fairness. And I would suggest that one should be slow before assuming that a term buried in the small print should be interpreted as imposing an obligation to carry ID and, if interpreted as such, should be regarded as fair when the mainstream documentation made available to consumers by the airline, such as the statements on the website, would seem to suggest that the carrying of such ID is merely advisory.

Saying one thing in mainstream documentation and something different in the small print would, it seems to me, significantly raise the likelihood of the latter being regarded as unfair. It seems to me that 7a33 is meant to enable BA to ask for evidence of entitlement to travel where they have reason to doubt that the traveller is in fact the person named on the ticket. I do not think that it should be interpreted as imposing an obligation on travellers to routinely carry ID and empower BA to routinely ask for such ID at will in the absence of any reason to doubt that the traveller is the person named on the ticket and, if it were to be so interpreted, yes, I think that it would have to be regarded as unfair given the far more ambiguous statements made by BA in its communications to passengers on its website.