The doubling cube works well in Backgammon because it is a rare example of a popular game with randomness, without hidden information (every information set contains exactly one node of the decision tree, if you want to get extremely technical,) and, critically, with "different endings" (normal win, gammon, backgammon.) Doubling decisions are especially interesting because while they're always objective (it could never be the case that perfect players disagree on the correct move, that requires nontrivial information sets,) it could be the case that:

- it's correct for a player to double and for the other to accept;

- it's correct for a player to double and for the other not to accept;

- the position is "too good to double," because the equity from the probability of a double or triple game exceeds the advantage you'd get from a double;

- all of the above being influenced by the match score, e.g. if I'm 3 points away from winning and you're 5 points away from winning, I could make different decisions than if it were the opposite.

Chess has none of them, the doubling cube would be exclusively a psychological power play, something like "it's theoretically drawn but I don't think you can defend it," which is not a great game dynamic.

In general, transplanting the doubling mechanic without a similarly rich context doesn't tend to work well.