I've done two breadths in History/Philosophy of Science and perhaps someone like you would find it decent because instead of analysing the so-called "lit BS" you would be analysing the philosophy behind the Scientist's approach, which is something someone with desires to pursue science may find at least a little bit relevant. (personally, "From Plato to Einstein" I enjoyed much more as in the lectures you just scratched the surface of everything and then only later chose what you want to study in depth for the essay. In the other one it was more specific case study which didn't tickle my fancy as much as I'm not interested in geology).
Secondly, do you really have to like literature to survive in Arts? I did Science and know hardly any chem or bio (did zero of that) and only like 2 physics subjects, rest all maths/some comp science/ logic(actually logic was an Arts subject lol, again I ask why?).