The thing that prevents using chords musically is intermodulation distortion - aka beat notes, if you're using musician lingo. In your rig (mostly your speakers), In the PA, and if it's loud enough, even in the ears of the listeners, if you play two tones, the non-linearities in the system generate difference frequencies - a 3rd tone who's frequency is the difference between the two tones. They also create a tone who's frequency is the sum of the first two frequencies, but that tone is less problematic, so we'll focus on the difference tone. Intermod is particularly prevalent at lower frequencies - the non linear excursions of loudspeakers moving decent distances makes this phenomenon very strong and important in our musical "turf".
So, let's say you play a low E - 41 Hz. If you also play an octave above that at the same time (82 Hz), the difference tone is 82-41, which gives us 41Hz - the same as the low E. You can play octaves all the way down on a bass, even to the low B of a 5 string, and it'll sound OK through most rigs, because the difference tone is in sync with the fundamental of the lower note.
If you play a fifth, the higher note is 1.5 times the frequency of the first. So, a low E is again, 41 Hz, and the A (a fifth above) is 61.5 Hz. The difference frequency is 20.5 Hz - that's really low. Your rig won't handle that well, it'll sound like mud. But move up the scale of the bass, and things get better - an octave higher, you get 82 Hz, 123H, and a difference frequency third tone of 41 Hz - that will sound OK.
One neat trick, using intermod to your advantage. On a standard tuned 4 string bass, when you're playing a D, a lot of the time, you wish you could play the D an octave lower, but you can't. If you play the D on the A string, and the A a fifth higher, the difference frequency that combination creates is....the note you wish you could play. Most (but not all) rigs willl do OK with that combination of notes. That double stop sounds thicker and lower than the D alone, and is a decent workaround to not having a 5 string for that partricular case. But go much lower thatn that with fifths, and you're back in trouble.
If you go to thirds, the frequency spacing gets closer - a minor third is closer than a major third, which enters into things.
The upshot of all of this is, the higher you go in pitch, the closer the musical interval you can play, and have it sound good. It's the laws of Physics, the limitations of your gear, and psychoacoustics that determine all of this.