Is it because the 5th has less chord quality than the root, 3rd and 7th so isn't missed.
I think this is very close to the mark, although I wouldn't say the 5th has "less chord quality" (all intervals have quality and I love all my interval children equally, I don't play favorites! Just kidding, #4 is obviously the best). But it's generally not a determinant of the overall quality of the chord unless it's raised or lowered. So the 5th is much more important in, for example, a diminished or half-diminished chord than in a more straightforward major, minor, or dominant chord (although the dominant quality is wide open for abusive alteration, as we know).
The perfect fifth is the closest overtone, in any pitch, from its fundamental after the first octave. So roots and fifths can blend in with each other so well that, depending on the instrument/orchestration, the listener might not even notice if the fifth is present in a chord voicing. That makes it a safe choice to skip if you need to do any textural cleanup. Sparser voicings in pianos/guitars can be powerful and useful, and they can be "cleaner" in an ensemble than a denser voicing. As you say, the quality of most chords can be established with the root, third, and seventh, in the absence of a diminished or augmented fifth.
Melodically, bigger intervals – while usually more challenging – can also be very powerful and effective tools. Melodies and harmonies that use lots of fourths and fifths can be really great and tend to be counterintuitive to learn, at first. Playing up and down a quartal guitar or piano voicing melodically on a saxophone can be a good way to practice incorporating larger intervals into improvised melodies.