Ctrl+Up/Down allow scrolling the text only, without moving the caret. However, the caret is moved if it goes off screen as a result of this scrolling (i.e. position it on the first visible line and press Ctrl+Down). There is no need to move it in any case, especially because with ScrollYCaretPolicy this causes the scrolling to jerk.
This is a Notepad2 (Scintilla?) behaviour.
Ctrl+Up/Down allow scrolling the text only, without moving the caret. However, the caret is moved if it goes off screen as a result of this scrolling (i.e. position it on the first visible line and press Ctrl+Down). There is no need to move it in any case, especially because with
ScrollYCaretPolicy
this causes the scrolling to jerk.