Sir Steven, I think I can explain it better with pictures. Yes, as you said, the last selected folder is indeed remembered under "Files" but it's not being shown as highlighted under "Folder View" because after a restart "Folder View is all the way back to the top again.
This is what MusicBee looks like just before exiting : On the left side "Rick Springfield - Greatest Hits" folder is highlighted under Folder View (left side) and all the songs are there in "Files" (right side)
Now after an exit and restart, it doesn't look like that anymore as you can see. The Folder View is all the way back to top again thus the highlighted Rick Springfield folder cannot be seen on the left side anymore. Yet all those songs are still there on the right side in Files thus a mismatch. MusicBee should be opening up the Folder View column exactly as where I left off, with the highlighted Rick Springfield folder on the left side and the songs to the right so your place (location) in Folder View can be easily seen and recognized. Sorry I am old, I hope I explained this well :-)