A degree is not a fallback; in five years time, if you've done nothing with it, it will in almost all cases be worth approximately nothing - regardless of subject. If you want a backup job capability, learn a transferrable skill like plumbing, cookery or TEFL.
A "foundation degree" is also worth approximately nothing if done in addition to CPL/fATPL, which are worth more, better understood, and the foundation degree contains little additional material, whilst the academic standards are minimal. I firmly class the Cabair/Kingston product in this bracket, even with the 1 year top-up to BSc Aeronautical Studies.
An "aeronautical science" (e.g. Leeds) type degree plus pilot training does seem, on the whole, to have some significant value in that there's a lot of experience that people with the combination fit into the professional aviation environment much better than those without. I don't believe, however, that the employers widely recognise this, so it'll not aid your initial job hunting. However, if you lose your medical, these degrees have little value in real science where they are generally regarded as "not real science".
An aeronautical/aerospace engineering degree with pilot studies is very tough and you really have to be interested in the academic subject, as well as the flying. There are careers where this combination works really well - particularly military flying: although those places seem to be dwindling into very small numbers nowadays. About 2/3 of test pilots nowadays seem to have aero-eng degrees in addition to either military or civil flying training. Plus, unlike aeronautical science, these are regarded as real engineering, and if you for whatever reason decide to stick with an engineering career, the flying training and experience is regarded as having significant value to an aeronautical engineer. This is probably the one case where doing the degree, then flying training, then going back into the degree subject, does not disadvantage you - because the aeronautical world tends to be more holistic: it's "all aeronautics".
G