But if they hit on a fifth and then the next interval is also a fifth, the effect is going to be that of two lines collapsing into one harmonized line.
Exactly! The same applies to parallel octaves.
There's a good page here that has lots of pictures and - more importantly - audio examples:
https://www.schoolofcomposition.com/whats-wrong-with-parallel-fifths/For a non-counterpoint example of the same phenomena, consider writing for 4 horns in a jazz setting. If you've got a chord progression like:
C | Am7 | F | G7 | CYou've got a mixture of 3-note chords (C, F) and 4-note chords (Am7, G7). If you double one of the notes on the 3-note chord so there are enough notes to give the 4 horns, you risk getting the same sort of "collapse" when the notes in octaves blend together.
To avoid this, you'll typically write
all the chords out as 4-note chords, so the harmony maintains the same 4-note texture throughout:
C6 | Am7 | Fmaj7 | G7 | Cmaj7The interval of the 6th in the C chord is neutral, so it doesn't change the harmonic function of the chord. The sound of 6th chords is a bit dated, but that's a different story.
