The exclamation thing does happen, though it doesn't indicate outside of camp that characters have things to say within camp.
In my opinion something like this is necessary and it should be noticeable... and it shouldn't just go away right away. There should be some kind of indicator that a long rest will trigger a story moment so that you don't just randomly miss part of the plot.
I don't mind if they make it a toggle or something - but it seems like this is an issue for almost everyone.
They should just add a yellow ! on the character portraits rather than an awefull mmorpg ! uppon our characters head (at camp but not only...)
This has been suggested months ago.
Same about OP's suggestion.
Players should CLEARLY understand that they won't become mindflayer soon... Or the game should be better balanced so players don't have to rest too much + have a coherent resting mechanic that doesn't allow you have infinite rests...
If you have to / can rest less often it looks a lot less wierd story-wise on top of making the game a better tactical turn base game...