I've just recently heard about people doing this to their dogs.
I guess it makes sense in order to have a companion, but it still seems kind of weird. If you want an animal that doesn't make any noise, why would you get a dog in the first place?
The main reason I detest birds (sorry Euph) is the noise they make. It might as well be "chalk on a chalkboard" to me, as their noise often makes me feel the same way. I would never buy a bird, then remove it's voicebox or whatever it is they have, just so it would not make noise. Why alter an animal like that, to accommodate my ears?
Makes much more sense to not get a bird in the first place.
Big difference between dogs and birds, and not just because one has feathers and the other doesn't.

Comparatively speaking, we know very little about companion birds, mostly parrots. We've not had the benefit of having them around us for tens of thousands of years, like we've had dogs.
In short, I agree with you about birds in that they can be (some species are actually known to be pretty quiet) quite loud. Considering that birds' are much more vocal than dogs are (dogs communicate largely through body language and they learn about their environment mostly through their nose and to a lesser extent, vision and hearing), I can't imagine having a companion parrot just to remove its syrinx. That would be cruel, because a bird very much does depend on what it's saying and more important,
how loud it is.
It's how they communicate in the wild, and considering that parrots are only a couple of generations from being in the wild, they haven't yet learned (and perhaps never will learn) to tone down their vocalizing to accommodate humans.
In short, if you have a potential problem with landlords or neighbors, don't get a macaw or a cockatoo. They're loud. But an eclectus, on the other hand, tends to be very quiet.
All birds are not loud.