playBunny: I would agree. I would not like Auto Move in Ludo. I could see it if I found playing games to be "work", but like you, I enjoy the process.
Also, I find it to be pretty rare that I only have one man on the field for much of the game. Of course it happens, but I find that through much (most?) of the game I have multiple men on the board.
I also would not like auto pass in Ludo, because of the same reason you gave, the board would potentially look MUCH different from the last time I saw it. I don't mind auto pass in backgammon, because I think it is pretty rare that as many moves would be passed, as could happen in Ludo.