Most guitar sites show chords in root position. For example, the barred A shape generally gets shown with X on bottom string - even though that's always a chord tone, including it gives 2nd inversion.
Why? Especially when those same sites show 'scales' which include all available notes in a certain position - those below and above the root - which actually aren't part of a 'proper' scale (starting/finishing on root).
Seems like two differing concepts.
This is for pedagogical reasons. In general, root-position chords are the most common, and when inversions are used, it usually sounds just fine to substitute with a root-position voicing (especially if you have a bassist or other instrument covering the bass notes). On the other hand, replacing a root-position chord with an inversion can create an unstable or even unpleasant sound if you don't give due consideration to the harmonic context. This is especially true of second-inversion chords, such as your example of an A chord with the low E string ringing out—namely, A/E. In an A major context, this chord doesn't sound "final." It sounds like it should go somewhere, as in the following progressions:
A | D | A/E | E | A A | A7/C♯ | D | B7/D♯ | A/E | Fdim7 | F♯m7 | B7 | D | E7 | AIf there is an inversion that you are trying to play and can't find on a guitar chord chart, it's probably because there isn't a good open voicing for it. Even fairly basic guitar chord charts usually include the open inversion chords D/F♯ and C/E, for example, because these are relatively easy to play and are common in guitar music. For a chord like E♭/G, there isn't really a good open voicing; instead you will play a generic shape for "major triad in first inversion," and figuring that out requires some theory knowledge that is readily available elsewhere on this site.
Especially when those same sites show 'scales' which include all available notes in a certain position - those below and above the root - which actually aren't part of a 'proper' scale (starting/finishing on root).
Seems like two differing concepts.
They are different concepts. A scale doesn't have a "bass note" in the way that a chord does. It has a root note, but this is a theoretical abstraction that allows us to give specific names to the different modes (E lydian, D locrian, etc.). There is no requirement that every instance of a scale contain the root note as the lowest note in the melody—otherwise music would sound strange indeed!
On the other hand, a D/F♯ chord isn't a D/F♯ chord unless the lowest note being played (by whomever is playing it; it could be a bassist or pianist instead of you) is an F♯.
If you're doing simple strumming, a root position chord generally sounds best. So this may be the voicing first offered to a beginner. That's all.
I think this is just a mechanical thing. It becomes clearer when you continue your point about an A form chord.
Start with and open E chord, transpose it up by fourths, add fingerings to include all six strings, note the available basses and inversions...
E 022100 root pos only A 002220 2nd inv & root pos D 200232 1st inv, 2nd inv & root pos G 320033 root pos only C 332013 2nd inv & root pos F 133211 root pos only (start of barre chords) ...
(If you do this same kind of transposing by fourth with a fully close position chord, like a C as 332010, the problem is even worse. The next transposing up would be F as 533211!)
Notice the problem when you get to C, you need to fret 5 strings! It isn't practical.
When you get to barre chords the E and A forms are practical, G is do-able with a big hand or high up the neck, but D and C form aren't practical. Those forms - E, A, G - allow for only root position or 2nd inversion. With no practical way to use all inversions, and with 2nd inversion being a harmonic special case, there doesn't seem to be a reason to go beyond root position in a chord chart.
Of course you can play inverted chord, but you need to skip strings, like x5x36x, and you would play with fingers instead of a pick.
