I noticed the same issue a few months ago. As a comparison the first inversion of the 7sus4 sounds correctly even though it has the same notes as the sus42 chord. (This does not mean you should use this particular inversion, because 6sus4 is actually equivalent to the second inversion of add9)
We figured out the problem. It turns out the music theory engine was interpreting sus42 as four degrees: 1, 2, 4, and 5, but the voicing algorithm was only voicing the first 3 notes. That’s why some chords were missing a 2, others a 4, and others 1 or 5 (which don’t technically affect the quality of the chord, since the bass voicing always puts a 1 on the bass).
We fixed the music theory engine to read sus42 as: 2, 4, and 5, which fixed the problem. We’ll roll out this update in the next minor patch of Hookpad.
Omitted fifth does affect the quality of the chord; I would be glad to use this sus42no5 chord if it combines with the melody to form appropriate 11no3no5 chords, but I guess that won’t come even in another major Hookpad update.
You could always internally force the sus42 chord to voice like the first inversion of 7sus4, seeing that chord has never broken the old or new voicing algorithm. It will not make any difference to those end users who could not find an actual 56sus4 chord in the editor (but you might run into more problems in the Trends API if all sus42 chords are interpreted as inverted chords).
I agree that the 11no3no5 chord is a pretty important chord in popular music that we are currently missing, and it’s certainly not out of the question that we would consider it in future releases. Our initial reservation about it was that it makes the most sense for V chords, and perhaps also works for ii, and vi, but doesn’t make a lot of sense for the other chords.
There have been multiple occurrences in Theorytabs where the 11no3no5 chord and its variations - transpositions of B♭m/C, B♭/C, Bo/C, or Bm/C - are forced to introduce dissonance due to the existence of the fifth, or use an incorrect bass in an appropriate add9 or 7sus4 chord, because the bass track is not independent from the chord track (although the mixer settings suggest that this may be implemented in the future). This does not happen in just few analyses, but in about twice as many songs as there are that use, say, V56.
The 11no3no5 does not appear in popular music only; both pedal bass and 2-3 suspensions in common practice harmony yield variations of it. Finally it does not matter whether 11no3no5 “makes sense” only for certain scale degrees, because as long as one form makes sense, it will appear on other scale degrees by borrowing from suitable modes, for example ♭VII/i or II/iii. It is the same situation that allows Hookpad users to put “true” Fsus4 chords in the key of C Major, and access the contrapuntal varieties that come with the suspension.