After having shot some 130 shots (most of them 48 Mpixel RAWs) today and having immediately sending some 30-40 of them: Indeed the 16.1 update has helped a LOT:
1, a LOT(!!!) faster RAW save times - you can take your next shot a lot earlier than with 16.0.x.
2, MacOS' "Image Capture" app now seems to be listing all images immediately and not after some hours / some forced phone reboots (note: I do NOT have any kind of iCloud image sharing; that used to be one? the only? reason for such a delay in my experience in previous major iOS versions. However, even with disabled iCloud image sharing (uploads), I've continuously been having problems with "Image Capture", the phone still being on 16.0.x, not immediately listing the last-shot RAWs when I tried to transfer the images to my Mac via "Image Capture".)
3, now, in iOS' "Photos" (I use Photos for Whatsapp sharing because Whatsapp can't select more than one image for sending at a time, while I can mass-select images in Photos and, then, share them to Whatsapp), if I (try to) share images too quickly after taking them, a progress modal dialog is displayed - that is, Photos doesn't seem to just refuse doing anything any more. (Real-life situation: I shoot flea market images into 48 Mpixel RAWs and, when I know a particular item is highly sought after some of my friends, I also immediately send them images via Skype or Whatsapp so that they can immediately tell me whether I should purchase the item for them. This way, I can avoid the item to be sold for someone else.)
On 16.0.x, if I too quickly did this in Photos, it just didn't do anything. This seems to be fixed now.
All in all, if you do shoot a lot and particularly RAWs, do yourself a favor and update!