The History of Rome podcast by Mike Duncan is over a decade (edit: typo) old but it's ideal for that. He has an incredibly relaxing voice, and even though I'm legitimately interested in Roman history I would find myself drifting off sometimes. The audio quality in the early episodes aren't great but he gets a better mic later.
I'd recommend the Welcome to Night Vale podcast. It's an audio play that presents itself as a local radio news station for a town called Night Vale, where all sorts of weird and spooky things happen but are all totally normal and mundane to the people there. It's very entertaining, and because all the "bits" are told like very short little news segments. Each story is pretty much self-contained and not intrinsically related to anything else, so it's easy enough to tune in and out while you fall asleep, and you won't really be missing anything "important".
"The British History Podcast" is also really solid for this.
There are also good ones on Japan, The Crusades, Rome, and the Byzantine Empire although I don't remember their names exactly. They're all variations on "The History of [x]" or "[x] History Podcast".
The history of the crusades one is done by an Australian professor and she's really good. I believe she did one on the Normans as well which was excellent, too.
Really, if you're going with History, I would do a bit of research on how they're perceived and make sure you like the narrator's voice. It's almost always one narrator which is perfect for sleep.
Additionally, I will go out and find lectures from "The Great Courses" series which are pretty well vetted for oratory because the speakers are genuine college professors. Just finished one of those on Balkan history which was really solid.
As far as vetting of podcasts goes, most of them are done by well meaning amateurs, but it should become clear whether they actually know what they're talking about. I'd recommend Hardcore History or Great Courses lectures as a jumping off point and then see about podcasts that are similar in respect for the subject matter.
Stuff You Should Know is a podcast by some well-meaning, curious, kind of dumb dudes from Atlanta. Libs but that doesn't seem to be a disqualifier. Anyways they have very gentle and calm voices and basically have done a straight up book report-style podcast for like fifteen years and have done basically every topic.
They have the right voices to fall asleep to because they never get so excited they change their register and seem to like each other. Kind, friendly energy. It's also easy to fall asleep to because you don't have to hang on every word because they usually don't really know too much about what they're talking about so it never really matters if you hear the next part because you'd have to fact check it anyways
I like Levar Burton Reads. His voice is so soothing. You can pick a story with a topic you are less interested in for nighttime listening since there are plenty to choose from.
I usually listen to any podcast with tech bros talking about tech because it is fun enough but completely inconsequential, so I don’t miss anything when I fall asleep.
Examples: Accidental Tech Podcast, Upstream, Cortex, Waveform
I love Startalk Radio for this. It’s very interesting, funny and they make breaks every couple of minutes with a jingle that triggers me to wake up slightly with enough focus to take my headphones off and then fall asleep
I really enjoyed Lore for a while until he got involved in his TV series. I feel the quality dipped a bit after that (but not a big issue if you're just falling asleep to them).
other similar ones for falling asleep to: Criminal and This is Love - Pheobe Judge has a great voice to fall asleep to. The content is interesting enough to have your mind not wander too much but her voice relaxing enough to lull you to sleep. I often end up listening to an episode over several bedtimes to hear it all. Hidden Brain is another great one to fall asleep to. The Memory Palace, similar to Roman Mars' narrating.
I like Roman Mars' voice so 99% invisible is my go to. But I'm still searching for a way to automate listening to British shipping traffic in a podcast like fashion.
Last Podcast on the Left. They talk about serial killers, but the subject matter doesn't bother me. It's a topic that I'm ok with not catching all the details after I fall asleep.
Damn, I tried to get into it years ago. It must be good because they still going at it, but couldn't stand the multiple mfs talking at once about random bs.
Yeah, I sometimes listen during the day and want to scream at the clowns to shut up and let the narrative move ahead. Luckily, I tend to go to sleep with a strong buzz or straight up drunk and then it doesn't bother me.
Smashing Security or Darknet Diaries. I always put them on before bed and fall asleep. I have to relisten from the latest bit I remember to make sure I get all the information.
Welcome to nightvale is great but maybe too interesting? It has a plot but I feel like it isn't that important. You can enjoy it without really following it too much
Clarkesworld Magazine and anything from Skyboat Media.
Kate Baker narrates the former, Stephen Rudniki a lot of the latter’s content and both deliver sonorous, resonant readings that are easy to nod off with.