Your question simply concerns the difference between first-order logic (where the distinction is maintained) and second-order logic / higher-order logic, where propositional variables are indeed simply variables, and therefore terms.
Early work (Frege's Begriffschrift, Whitehead and Russell's Principia Mathematica) used stronger logics, while first-order logic was isolated later. FOL is no "better" than those stronger systems, and indeed higher-order logics are generally preferred for interactive theorem proving.
More discussion here.
