I agree it is a worthwhile and engaging mathematical activity for young students as originally presented for the reasons you outline. That is why it is so important to transform it into a real game with some choice/ strategy involved (because to be a ‘real game’, it needs to have these things)

I like Pinocchio because it works on two levels - because in a sense a game like Snakes and Ladders is deceiving you ‘masquerading as a real game’; but you can also imagine it ‘wanting to be a real game’ if it had agency

I think this is an interesting idea. Perhaps you have three such tokens to play in the game, and the snakes and ladders can only be moved to a square not currently occupied by one of the players

Depending on the year level, a further variation of your second suggestion is to roll 3 dice, choose the 2 you wish to sum together, and to move that many places.

Can you think of any other 'Pinocchio Games' that could be tweaked and transformed into real maths games?♾️

Snakes and Ladders is a 'Pinocchio Game'. It wants to be a real game, but it's not because there's no choice, and thus no skill/strategy. How would you tweak Snakes and Ladders to turn it into a 'real game' to support the teaching and learning of number?