This is a silly argument because pop notation and classical notation are clearly different. In classical notation, there is no such thing as a slash chord in the first place! But in pop notation and chord charts, it is very rare to see the classical notation for inversions (6 and 64 for triads) used; rather, they always use slashes to indicate that the bass note differs from the root, whether or not that bass note is a chord member. This is done for the sake of fast sight reading, especially since an average pop musician does not know classical notation.
From a theoretical point of view, yes, the inversion symbols make much more sense than the slash chord system, which does, in a way, kind of suggest that the bass is a separate entity from the chord. But the idea is that most casual pop musicians don't know jack about theory, so the slash chord is a short cut for the LCD (musically speaking, of course; I am not equating ignorance with stupidity by any means).