The thing you want exists. It's called the Fediverse. Don't like the politics? You wouldn't have liked Usenet in its heyday either.
For the most part, when people talk about "The Fediverse" they mean ActivityPub based sites. You could argue the point, since NNTP is "federated" as well, and one could certainly conceive of federating between the NNTP space and the ActivityPub space.
I'm a Fediverse user, fan, and advocate (mindcrime@fosstodon.org), but I specifically mentioned Usenet, because the "thing I want" in this context is, in fact, Usenet. Now if somebody wants to do the work to rebuild the Usenet hierarchy on top of the "wild west" that is the litany of servers on the Fediverse, build client support into Thunderbird, etc., then sure... that could probably turn into something interesting.
You wouldn't have liked Usenet in its heyday
Please don't presume to tell me what I would or wouldn't like. That's incredibly disrespectful. And in point of fact, I did like Usenet in its heyday.
Interestingly, this seems to be amongst the most controversial aspects; some people _hate_ it.
Personally, I was only quite dimly aware that Twitter had an algorithm now, like a common Facebook; until Musk ruined it I generally only really used Twitter via Tweetbot, so was getting a time-based feed anyway. So Mastodon was just what I was used to anyway. But more people than I expected actually liked the Twitter algorithm, and couldn't cope with Mastodon's lack of magic ML stuff at all.
With Usenet, if you join, say, comp.ai, you know that (spam aside) you're just getting AI stuff. Same for comp.linux, comp.lang.c++, or whatever. There's something to be said for the topic hierarchy there.
I see a place for both ActivityPub and Usenet, personally. Although, again, acknowledging that somebody could probably in principle build the Usenet style experience on top of ActivityPub. But as far as I know, that part doesn't exist today. If it does, somebody please let me know.
Yes, having images available within mastodon is nice - that was always clunky with usenet.
When I used it it seemed like it was mostly real names (.edu accounts) at least on the groups I read, so maybe that kept people in check a bit. Though that would have been easy to spoof I'm sure.
My department also had some local groups that did not propagate. So it must be possible to stand up your own NNTP server and have groups for your local users that are at least in that sense "private"
I don't think the Usenet model can be replicated on top of Fediverse. Not everyone sees instances as a topic thing (I host my own instance).
Since it's all ActivityPub, you can follow Lemmy communities from a Mastodon client but the UX in that case is pretty bad (e.g. Mastodon servers won't backfill posts so you won't see any history).
There's a newsgroup still extant which is named after a woman who spoke up about the CSAM problem on our local university's server (I stumbled across it myself once, there was some nasty fucking shit going through there). The users of these groups did not take kindly to people messing with their access to pictures of children being sexually abused. Not naming her or the newsgroup because I'm sure she's long since gotten it in her rear view mirror.
Also, some quirky usenet groups aren't available elsewhere, such as alt.binaries.*
Or just join an instance that is not explicitly political. You don't have to be on beehaw or hachyderm.