I have a DC interested in the Birmingham LANS course. Obviously the draw is that, potentially, you can have a mix of subjects in a ratio that appeals to you.
However, as OP flags, in this case you have to guard against shifting it unintentionally from NatSci to LANS on the degree certificate and diluting the Phys element so that it is less meaningful to prospective employers and the student themselves.
Another aspect to consider is that there are compulsory LANS units in Y1 & Y2, potentially 'squeezing' space between 'core Phys' (in the case of OP's DC) and the LANS units. That said, the LANS units look very interesting their own right and are design to bind the LANS cohort together, which is a particular attraction of Birmingham's approach.
With reference to prospective employers' reactions, it is for applicants to make the case that their degree makes them different in a good way. At the very least, successfully completing a 'composite' degree requires a strong independent spirit and fantastic time management skills!
There are several northern unis offering NatSci in various forms (Durham, York, Leeds, Lancaster off the top of my head). These tend to be more structured to ensure prerequisites are covered off and have limited/no scope for non-scientific modules.