Well, the samples provided in the discussion so far have been in a "traditional stack of thirds harmony". It's not that we don't know other perspectives, we're just using the relevant perspective here. Your generalisation is useless.
I guess you mean "non-chord note and chord note in the bass", not "non-root note and root note in the bass"? If the root is in the bass, there is no need for a slash.
My point of view is anything else the useless. Maybe useless for you because you have your own perspective that, in my eyes, is a bit limited. Or you define a slash chord different than me.
I have done a lot of transcriptions of piece that use slash chords with the root of the chord lying in the bass note. It is not too common and not used in the great American jazz tradition (except if one player is able to put some of them in).
Analyse some earlier Jan Garbarek tunes, i.e. Places.
You can notate that without a slash with a lot of of "alterations" (there is nothing altered in the scale, it is just very different from a major scale). So a slash chord might be easier to read or it shows what voicing should be used (as in my example) which was explained by others here too.
OK in a full chord (6 to 8 notes, depending on the scale) every slash chord could be seen as an inversion, but how much sense does it make to see a b13 in the bass if it is not part of a linear movement of bass notes? And specially if you hear this note as the root of the chord.
I know that my perspective on slash chords is correct as I discuss this with composers and advanced theory knowledgable jazz musicians. I know that this is not accepted by a lot of people, but this is often the case with new stuff (and I don't think my perspective is real new, just a bit more analytical).
In my big band arrangement I wrote the slash chords for all accompanying chord instruments, but for the solo parts I also wrote full stack of thirds chords for those who can work better with that. It is more that most people are not used to analyses scales from slash chord notation, so it might be some help to see that in a more traditional manner, but to see through all these many "alterations" might take too much time. BTW, I also add a scale notation to the root/bass note to show what scale could/should be used. So G/Ab hMaj VI means the structure of the sixth mode of harmonic major starting from Ab. If the chord root would be the root of the upper chord I would notate the scale before the slash.
Like it or not, this is an effective notation for scales if you want to fix them. If not, it would even be a starting point for the typical scale that would get used there. Since slash chords are not full chords, there are several other possible scales (usually). But different ones than you would use with a three or four note stack of third notation.
I was prepared for some discussion here, but not for ignoring it and declaring it as totally unrelevant.
I am happy to discuss, but only if people do their homework first.