Vikings: Well, all 'information' such a button (which would probably never materialize) would reveal is "you only have one move available', or, in its absence, 'you have more than one move available'. It's not going to reveal anything about opponents pieces, or whether you have more than two moves available.

Not that I think it harms the opponent to show a player the list of available moves. A determined player can already find out all moves he/she can play; first by hoovering over his/her pieces (to see which pieces can be moved), then by clicking all moveable pieces and see which fields are clickable (destination squares for the pieces).