There are tons of useful features that aren't supported in C. The basic feature set of C was determined by whatever operations Dennis Ritchie could easily implement on the PDP-11 when he created the earliest C compilers. (Fun fact: the bitwise operators even preceded the Boolean operators like && and ||.)
If the question is "why isn't bit indexing supported" then "because processors didn't (and don't) support it" is the historically correct answer, whether you like it or not.