Hmm, maybe that episode of Dateline not showing up next-day was a fluke or maybe you were on the free tier of Peacock at that point. To the extent that current NBC shows are available on the free tier of Peacock, I think they're on a one-week lag, whereas they show up next-day on the paid premium tier (same as they do on Hulu). This article had the run-down for last year's 2020-21 NBC season.Yes you can watch The Blacklist on the cable-authenticated NBC app next day but you are forced to watch ads. Pretty sure it was early last fall season where I wanted to watch a specific episode of dateline but it didn't get to Peacock for a week but it was on the cable-authenticated NBC app next day with forced ads just like The Blacklist. That might have changed in the last year though. I canceled Peacock a few months ago anyway because there just isn't much on NBC that I watch and I found their other stuff didn't really interest me.
I get Peacock Premium for free via Comcast broadband. I wouldn't pay for it but I have found a few things on there to watch. The ad breaks are mercifully short. As for NBC itself, the last primetime series I watched on it was Superstore, which is now done. Only stuff I care about on NBC now is SNL, the evening news, and occasionally Meet the Press. I DVR all three from my OTA antenna. At times when I have Hulu ad-free (like now), if I don't catch SNL as it airs live, then I watch it next-day on Hulu since it has much better HD picture quality than NBC OTA, plus there are no ads to FF through as in the DVR recording.