I mean, if you don't trust the computer to look after your interests with regards to your voice interactions, why are you trusting it when it also controls life support and airlocks? ;)
Like come on guys, there's more than personal logs. There should be more barriers before you go there. But to also be fair, it is stuff they know is going to be used in that way and it isn't just a log of everything they've said in their room. So there is a little more consent involved. I don't think you can really give consent to always listening devices.
Which is appropriate. There's nothing wrong about locating a crew member on a _military vessel_.
This is the highest probability of the realistic outcome of AGI as it will advance in capabilities so much and so rapidly that we won't be able to keep up. I personally think it will be benevolent and care for us like we do for our pets which won't necessarily be a bad thing.
We are still very much savages. Clinical psychopaths and delusional narcissists run our institutions and major decisions are made on the basis of fanatical superstitious ideologies and mindless herd behavior.
In short I won't put an Internet connected microphone in my house and I'm very wary of privacy leakage in general because I don't trust the people who run our world (including both governments and corporations). I don't think this is irrational. Glancing around it seems like a decent number of world government and corporate leaders belong in prisons and mental institutions, not powerful offices.
But also portrays societies run by and indeed composed entirely of mobsters (see "A Piece of the Action" TOS S2E17).
Interestingly, while this is certainly the background assumption of Star Trek, it is much less valid in episodes where the crew must interact with their own government.