Currently it's a hassle to manage your label classes from the layout view - to use list by labeling in the TOC, you either have to keep activating/deactivating your map frame or opening the map in question and going back and forth. It would be very convenient if the list by labeling tab of the TOC just stayed with you when you switch into the layout view, showing the labeling classes of the active data frame. A frame/map selector at the top might be a good addition, or leaving them in a scrolling list similar to the drawing order view or ArcMap would be useful -- you could easily copy & paste label class properties between maps in one pane.
ArcMap actually has no differences in the TOC options between map and layout, and the consistency there is very nice - nothing is suddenly gone when you switch views. While some of the new options in Pro are very helpful, it would be more helpful if it were more consistent. Pro took a step backwards in this regard.
List by labeling is the one whose absence in layout is most frustrating to me but there may be use cases for the others to carry over there as well. I do a lot of work with my layers while in layout, but Esri (Pro especially) seems increasingly focused on this abstract idea that there is a linear process to mapmaking -- data > map > layout > print. In practice, this is not how things work at all. Good design, good data visualization, and good mapmaking each requires a lot of back and forth, but Pro generally induces much more than is necessary. Anything to reduce that and make things happen in less clicks would be welcome.
