So the question is a good one, and can't be answered with 'tough shit' quite that easily.
With a mature UBI, there's still certainly room for cases where there is ambiguity over whether culpability of the form represented by a criminal prosecution for abuse/neglect exists, but a lot less room for ambiguity (at least, compared to now) over whether there is a sufficient failure of basic parental duty to justify intervention to ensure the material adequacy of care for children.
> In the UK, a recent report suggested that child services spend so much of their time chasing the former, that the latter cases (which are much more serious) don't get the attention they need.
That's definitely true in the US as well. I don't disagree that these services need to be reformed and reprioritized, independently of the nature of the public benefit system.
But the problem with beneficiaries (parents or otherwise) blowing or trading their benefits without meeting their and/or dependents material needs exists independently of the nature of the public benefit system -- its quite clearly a feature of the status quo system -- so its not really an argument for or against any particular public benefit structure.
I don't propose that, both because I think the size of the problem that would be addressed this way is no larger under a mature UBI than it is today (even if UBI makes the responsibilities more clear), and because I think a mature UBI would reduce other sources of children entering the system (both by reducing the social problems which result in children ending up in the system, and making it more likely that alternate, extended-family placements which are generally preferred could be found to keep children experiencing the kinds of problems which could result in them entering the system out of the system.)
Seems to me that with a universal unconditional benefit that is sufficient for adequate support of both parents and children (which, incidentally, I don't see as likely in any early-phase UBI, though over time it would hopefully grow to that level), failure to provide adequate support for children is, without exception, culpable neglect; interventions to address such neglect exist and are outside of the scope of the public benefit programs UBI would replace (though, if children are counted as beneficiaries with the benefits flowing to their legal guardian, you've dramatically simplified some aspects of the administration of those programs, as well, with a UBI.)