I can't say anything about the history, but @Peter seems to have that covered in his answer.
...To Slash or not to Slash?...
If you have only one accompaniment instrument - like a piano or guitar - which needs to handle the bass - or if you are the bass player - you should be mindful of the inversion indicated by the slash. Someone filling in the middle while a bass instrument deals with those inversions has more latitude to not use the proper inversion.
While pop styles seem tolerant of 'interpreting' the chords with substitutions, different voicings, etc. classical style really doesn't allow that latitude. I suppose I am a biased snob, because I feel you must play the right inversions. Can you imagine playing highway to Hell without the slashed D/F#!
The choice also needs to be tempered with an understanding that many song books list the wrong chord symbols. I've seen many slashed, added, and sus'ed chords that are obviously wrong compared to the recorded arrangement and inexplicably try to represent non-chord tones in the melody.
So I think there is room for interpreting, but I think essential inversions should be recognized and played as indicated.