The sound /ʑ:/ is known as the voiced alveolo-palatal sibilant fricative and, roughly speaking, is the average of /z/ as in zebra and /ʒ/ as in vision. Russian speakers can understand /ʑ:/ as the voiced counterpart of щ or, alternatively, as the soft counterpart of ж.
Until recently I thought that the sound /ʑ:/ occurs in Russian only in a couple of rarely used words, namely дрожжи and вожжи, but a few days ago a Russian speaker told me that the sound is much more common, referring to визжу, брюзжу, дребезжу, размозжу, and брызжет as examples.
Curious, I tried to find an exhaustive list of words with that sound, but did not succeed.
My question: How prevalent is the sound /ʑ:/ in the Russian language from a native speaker's perspective?
To clarify, I am curious as to roughly how many words you pronounce with that sound - a few, a few dozens, or much more than that. If there is an exhaustive or nearly exhaustive list of these words, I would like to see it. I am also curious whether the prevalence of this sound is dialect-dependent. Finally, if this sound is quite common, I am curious why there is no own letter for it, especially as its voiceless counterpart has its own letter, щ.