The in-universe answer re: drones would be that people want to explore. Sure, it's dangerous, but it's also exciting, fascinating, and fulfilling. That said, I feel like a responsible captain would make much more extensive use of probes than any of the shows.

Re: data streams, I don't have a good in-universe explanation. I have a similar question of why they don't have security cameras in all the hallways and public areas.

Also, using the transporter to go down to a planet always runs the risk of some storm or an orbital threat stranding your party. Why not use the shuttle as SOP? It gives your away team more resources, both for their mission and for an emergency.

I can't remember who said this in the show in Universe; maybe Janeway? But I think a similar question was posed, and the answer was that nobody would have anything to do if exploration was entirely automated. It's fun and exciting and gives people's lives meaning.

My headcanon is that many mundane things are automated, and we don't see them because they aren't plot-relevant.

I've always said that Starfleet is, first and foremost, a jobs program.

It gives purpose to people who can't find their own, in a time where your needs are provided-for by default, and seeking personal fulfillment is the purpose for most people's lives.

Drones would cut out the human driving a shuttle over to inspect an anomaly or object themselves, robbing them of a sense of accomplishment and achievement. Starfleet is about that stuff, so that's a no-go unless nobody wants to do it and it needs to be done anyway. We see that a lot, too. They do have probes and sensor stations and stuff, after all, usually in really boring and unfulfilling locations.

They have excessive, ridiculous redundancy. They have people doing jobs the ship computers could (and often, in times of need, DOES) perform very well on its own. There are several recorded instances of entire starships being successfully maintained for extended periods of time by a single individual (who does go insane due to isolation every time, because plot).

1 argument against the use of drones:

No one's going to watch a realistic exploration sci-fi show about small unmanned ships quietly going about their jobs with no drama.

They tried to, but the exocomms became sentient and they couldn't be used as slave labour anymore.

You forgot to add "Are they stupid?" at the end of the post title

Why aren't they using drones

They use probes all the time... Those are basically drones. But better.

Also: The Borg have several drones. 😏

In a similar vein, I've been rewatching TNG and find myself thinking that they really should have put a cctv camera in engineering. Could have saved them a lot of trouble.

Why invest in tech when there are so many red shirts around?

Probably because the butlerian jihad forbade them.

They aren’t?

Enterprise sends out probes (drones) just about every other episode, especially in TNG. Almost everything is automated on the ship, controlled through the computer interface.

Drones can't negotiate the if they trespass or make accidental contact in uncharted territory.

In the original series episode I just watched, they reference that they've sent out tons of unmanned drones/probes to map out systems and planets, but starships are enormous and better equipped, so they follow up on any readings from the probes that seem interesting. If there's an in-universe answer that isn't "it makes better television", I'd say it's a combination of:

1. Space is really, really big, so probes are only covering small areas anyway.

2. Their mission is to explore and contact new life, which is more likely to be successful with a human touch.

The Amazon drone wars of 2032 is still a touchy subject in the future

It's fun to see what modern tech is missing from decades old Sci-fi.

One of the most interesting ones for me, is that there aren't any screens with text on them shown in the original star trek. That's because when TOS was made, computers communicated by teletype/printout. TOS is older than the concept of text on a screen.

That said, I feel like a drone would be part of a tricorder. I have a DJI drone with a good camera, and I use it a lot for getting pictures of things that are out of my reach, if you had one paired with a tricorder, you could look at things out of your reach.

I mean, the Borg are right there on the poster!

They live in a post-scarcity world with insane science fiction technology, but they keep the executive decisions in the hands of crew members.

I know this is how people in the 80s and 90 imagined the future and a lot of concepts were probably too far fetched for them.

You also have to consider that TV executives were also considering this, and punting any ideas they thought wouldn't be accepted by a TV watching audience of the 80's/90's. Like the planned gay characters who were scrapped.

I mean, think about that, being gay in the future was too much for some television executives to accept, I really wouldn't be shocked if they gave thumbs down on lots of more esoteric and abstract episode concepts simply because they thought it would be too above the heads of a 90's TV audience.

And to be fair, they were probably right. The communicator seems less amazing now that we live in a world with cell phones, but back then a personal communications device that was on your person at all times seemed definitely in the realm of sci-fi. Now we all have a near-equivalent in our pockets, as well as it being general purpose computing device that can be used as a personal communicator and much more. Our communicator is also a primitive tricorder.

Some of the ideas they did let pass were either already accepted tech from the original series or were close to existing civilian or military hardware that was in it's infancy.

So a combination of "this was the extent of human imagination about these concepts back then" combined with "television executives are keenly aware of ideas the general public won't understand, and doesn't like confusing audiences, and thus will cut any content they deem too abstract or confusing" is what I think actually happened. One part actual limitation of imagination, one part purposeful limitation of imagination as to not to confuse the audience.

Which, honestly, is fair. Do you think sci-fi series like Rick & Morty would exist as they do without all previous sci-fi series laying down frameworks we understand for it to be based on? Human knowledge and ideas do build on themselves, and so, in a way, the TV executives are half-right that you can't overexpose an unexposed audience. You kind of have to slowly spoon feed them ideas over time.

Like, what if we tried sending Rick & Morty as a show back to the 1960's, and how many of the ideas would be entirely over the audiences heads? Simply because they didn't have 60 years of sci-fi media relating different iterations of these various ideas until "the multiverse" is just talked about like it is just a given thing that exists, and nobody questions it. At least a few would have trouble wrapping their minds around it, because while many of these ideas were pioneered in the Original Series, their lack of depth might leave audiences back then really confused about some of the ideas presented.

The same reason all the top ranking officers go on all the away missions; so the show isn’t boring.

What's up with Troi's nose?

PIC touches a bit on this subject, spoilers ahead:

The first season has artificial intelligence and the attempts to (re)create a true artificial life form like Data as one of its main themes. Also an explanation why it isn’t and hasn’t really happened so far, anywhere in the quadrant(s).

There is also the stated reason that simply cataloging space with probes or so is not enough, mankind (and in extension, starfleet) consider in-person exploration much more rewarding and fulfilling, and a worthy occupation in itself.

As for data streams from their away teams, yeah that would certainly make sense. Even today's military is essentially fully online. Camera and audio feeds, gps access, depending on the soldier’s function full drone control suites, various other situational devices.