Live Chess -- Game Examination Suggestions

When observing a Live Chess game, particularly if it's bullet or blitz, I find it irritating that the board updates after each new move when I try to look at an earlier point in the game.  Even Daniel Rensch appeared to be a bit flustered yesterday during the Magnus Carlsen simul when encountering the aforementioned issue.  It becomes a headahce if:  1.) I hop in late to a game and want to check the opening;  2.) I miss an important sequence and want to go back; 3.) I don't understand a tactic and want to take another look; etc.

Also, I have one more smaller point to bring up.  In the Live Chess interface, it would be very nice if one could use the arrow keys to go to the next/previous move, similar to how it works in Online Chess or the Analysis Board.