Okay, after studying this for a bit:
What we'd like to have is exemplified by
https://www.youtube.com/watch?v=qcvTHQxBcLw(after 28 seconds or so there's a voice exchange). There's little static, but the voices sound flat and perhaps a bit metallic.
I'm not sure what exactly was in the Shuttle vid you have seen - I have no simulation of static in, it used to be that the aircraft com instruments produced some when a transmitting station was overflown (frequency match but distance too far), but this should be gone now as the Shuttle doesn't use a standard aircraft com stack.
Only the minority of voice callouts done by the system are intended to simulate 'real' communication with mission control, many are advisory messages, limit warnings or failure notices. There is filtering done, so we know for every message what it is.
It would be cool to get a list of real messages and record them with the right distortion - but unfortunately some of them need to be assembled dynamically (like when you get burn parameters transmitted).
There's still a sizable chunk of standard messages and callouts which could be pre-recorded.
I guess in summary, I'd very much like to have improvements in the sound, especially in the group of real voice com, but I don't really know how to get there all the way.