Well, still, one would think even a limited automaton would have uses for uninteresting jobs that we see crewmen performing.
Then again, we don't really see people performing boring jobs... and one might argue that in the 'enlightened' age of Trek that no one finds their job boring.
Well, we know O'Brien found standing in a transporter room all day, every day boring as hell, and was happy to get the exercise of constantly patching DS9 up
At the same time though, if you were going to use an automaton to play transporter chief, why bother with the robot - why not go straight to runabout-style voice commands-only? Presumably there's something necessary - or at least highly desirable - about manning the transporter rooms of large ships with sentients.
We have the technology today to take off, fly and land an airplane without human assistance.
People are there in case the shit goes down.
As for why there aren't more positronic AIs....
I'm assuming that (in Trek at least), the only known method of achieving the kind of co-dependent, parallel, learning, "natural" intelligence is to use a positronic circuit, or later a holographic matrix. Probably something to do with complexity.
The positronic net, however, is like building a very flimsy house of cards. Only one in a hundred examples actually succeeds, even if you're doing everything the same every time. Even Data was unable to successfully replicate his brain for more than a few days. So while it's basically the only way to create a truly sentient being, it's also damned near impossible to do by its very nature. Like balancing knives end to end. Maybe as time goes on they'll create a technology to do it reliably but obviously 30 or 40 years hasn't been enough.
There might be a morality issue of creating and inevitably having to dispose of dozens or hundreds of artifical intelligences in order to get a stable one, somewhat akin to the modern debate about creating embryos for in vetro fertilization.
In the novels the Federation has basically given up on positronic based AI and instead employs holograms everywhere, to the point where yes, there is a "slavery" discussion as it becomes apparent that some of them are gaining natural sentience.
Why they don't make a rule that holograms must be turned off and rebooted X times a day to prevent sentience is beyond me. They do it to droids in Star Wars. Holograms certainly don't start out that way.