uh, my understanding "and hobbyist understanding at that" is that "slash chords" as they are popularly known.... (chord inversions, to the sticklers?)
a Dmaj is a Dmaj is a Dmaj... regardless of which of those 3 notes are played in whatever octave...
the root (1st) is STILL the root, and just becuse you "open up" the chord and stick one of the component tones into the bass... the root (1st) has not changed...
on basis of YOUR "handy notation" system you have developed... you are implying that a D and a F# are somehow the same chord, perhaps interchangeable?
heck, following that to some conclusion, if a piece is written in D, I might as well play it (transposed) to F#... after all, its the same thing...
a Dmaj is till a Dmaj... the slash inddicates which tone is in the bass to avoid confusion, not create more. the three discrete tones that make that Dmaj chord make it up, and none other... but particularly on guitar and keyboard, this gives you many options for how you voice that Dmaj chord if you are going to be hitign it a lot, and it might sound repetitive...
allows you to sound to the layman as if you are throwing all manner of chords in, even though all you might really be doing a simple 3-chord layout for the base structure before you dress it up...
I have a sense one could perhaps deliberately slash a chord to a particular inversion, as a pretext to a sudden unexpected series of chord changes, perhaps to set it up better, but, I lack any skill at that, lol... I am completely wthout any skill at making interstng changes. its my price I pay for now by not playign guitar and/or piano... I know good keyboard players (and I must assume guitar players...) can take a standard 3-chord format and "wal mart" relative brideg setup... and play the thing thru always usng chord nversons in a novel fashon to get a more complex sound out of the basic piece they are given...
uh..... huh-huh-huhhhh... er, or, like, SOMEthing like that...
but its all cool.... I only fuss over what litle theory I do know, because I have no talent...