You have a point, but on the other hand once one knew the notes were private, or if one correctly assumed they were from the beginning, the constantly seen "private" would be superfluous and annoying.
Already similarly annoying now is the rather lame yet constantly repeated joke "Scribble", and the lack of consistency over the three panes. If the three-point ellipsis isn't necessary after "Type a word here" in the Dictionary pane, it isn't necessary after "Type notes here" (distinctly preferable to "Scribble notes here") in the Tools pane either. Furthermore, "Type reply here" should be restored to the Chat pane as in the prior version. Thus:
Chat: Type reply here
Dictionary: Type a word here
Tools: Type notes here
The only reason I can imagine for the deletion of "Type reply here" in the Chat pane of the new version is that some bright person thought, "Aha, but the first chat text isn't a reply!" and so deleted the line entirely. Better – and presumably still doable – would be to program it so that "Enter chat text here" changed to "Enter reply here" following the first entry.
Not that there's much chance of this simple corrective enhancement being implemented, though I would enjoy being proved wrong.