I think we often find misuses of the terms in music. Sus chords will not contain the 3rd. All other extensions do contain the third. An 11th or 13th or 9th chord by definition will contain the third and one often sees voicings that will sacrifice most other notes to save the third. A common 13th chord voicing on the guitar just has (1, b7, 3, 13) and no 5, 9 or 11 even thought they are in the spelling of the chord. You bring up a very interesting point in that the function of the X sus(4) is a suspended resolution to X maj, and an x sus(2) suspended resolution to x min, but I don't think that function must be realized to preserve the naming convention of the chord. I've seen pieces that end on the I sus rather than I, just to leave the listener "unsatisfied" as an artistic decision. In modern music, especially rock, sus chords are sometimes used as is as the primary chords in a song without even moving the sus to the 3rd. But I would say that the naming convention should be preserved.

I think we often find misuses of the terms in music. Sus chords will not contain the 3rd. All other extensions do contain the third. An 11th or 13th or 9th chord by definition will contain the third and one often sees voicings that will sacrifice most other notes to save the third. A common 13th chord voicing on the guitar just has (1, b7, 3, 13) and no 5, 9 or 11 even though they are in the spelling of the chord. You bring up a very interesting point in that the function of the X sus(4) is a suspended resolution to X maj, and an x sus(2) suspended resolution to x min, but I don't think that function must be realized to preserve the naming convention of the chord. I've seen pieces that end on the I sus rather than I, just to leave the listener "unsatisfied" as an artistic decision. In modern music, especially rock, sus chords are sometimes used as is as the primary chords in a song without even moving the sus to the 3rd. But I would say that the naming convention should be preserved.