I feel like most of the crime podcasts (Serial, S-Town, Dr. Death, DIrty John, other Wondery podcasts, etc.) just dive right into the stories. No banter at all. And if those don’t catch your attention, there are plenty of college admissions podcasts! 
Oops, on the listing in the first post @Lindagaf !!!
@Lindagaf Glad you are enjoying the dulcet tones of Dan Carlin:). I know you said you have listened to This American Life in the past, but in case you missed some of the older shows, two of may favorite podcasts ever were the episodes on Testosterone (220) and The Psychopath Test (436). I really love it when a podcast shows me that what I think I know is just plain wrong.
@kbm770 , can you give me a few suggestions on those?
I love, love, love Imagined Life on Wondery. It takes you on the life journey of someone famous - could be in medicine, politics, entertainment, business, etc. and you live their story as if you’re them. All the while there are hints about the person’s life, and while you are guessing in your mind who it is, you don’t find out who “you” are until the last few minutes. They have some really interesting people… and my co-worker and I go back and forth on it.
I second Dirty John, Dr. Death and Over My Dead Body. Those are great, too. I’m currently listening to The Dating Game Killer…taking a lot of walks to get these podcasts in
@Lindagaf, you mean college admissions podcasts? There are SO many but the ones I find myself listening to are Getting In, The College Prep Podcast, and, sometimes, Inside the Admissions Office. They information may well be old news for those who have been through the process, but as our oldest is a junior this year, I find much of it helpful, or at least interesting. Of course it’s easy to skip topics that aren’t relevant to us. I tried a few others but wasn’t as drawn to the hosts (lots of chit chat!), and honestly, there are only so much college admissions podcasts a person can listen to!
Over my dead body is a good crime podcast. Agreed @kbm770!
I also listened to Cold which is about the Susan Powell disappearance. That case is crazy! I see it was already mentioned, it’s good but it is long
Fivethirtyeight is my favorite. Could match your NPR interests.
There’s perhaps 20 seconds of a non serious “cut” at the beginning but no chit chat. Because I’m a nerd, it’s the only podcast that makes me laugh out aloud, even though the basic framework is data journalism (polls, stats, trend analysis…) and thus probably not what most people consider funny. 
Wow, you all are great! Now I can wade through the garbage! Will I still have time to read books?
OP, I’m with you - just don’t like that chatter at the beginning of podcasts! I’m always on a hunt for something good so I’m watching this thread closely!
Have you listened to “Bear Brook”? It’s a true crime type podcast; H and I really liked it. We like to listen on to podcasts during our “regular” 15+ hour drives back and forth to our beach house. This one kept us listening through a lot of states!!
There was a podcast related to the Coronavirus that a poster recommended on this board. I couldn’t wait to learn more, but the podcasters started with the chatter, and it went on for so long, I lost interest. I think it might work if you, as a listener, have established an affinity for the podcasters. I can think of a few podcasts I listen to where there is some chit chat at the beginning, which I enjoy, because I know the personalities.
Podcasts have to be heavy on information for me to stay tuned. One of my regular podcasts, which I won’t mention because it’s political, goes on for an hour and a half, and usually loses me after an hour. I don’t enjoy listening to speakers having a good time with Teach other. Just the facts, ma’am. They really need to consolidate the podcast into 45 minutes or so.
Most of the podcasts I listen to are political, so won’t recommend those. My next favorite genre is crime, and they have all been mentioned so far, except for The Vanished Podcast. Marissa Jones takes a different missing persons case each podcast and reviews what has been investigated so far. I try to solve it as I’m listening. She covers all angles, and then gives her own personal reflections.