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Hardest/Impossible Composition Challenge?

Here is a challenge I've been thinking a long time about. It might be impossible but I can't be sure since I never found a counterexample or a proof.

CHALLENGE:
Create a chess problem (in regular chess), where one of the moves has to be an underpromotion to a Rook or Bishop, and the purpose of the underpromotion is not to avoid stalemate.

Note: The underpromotion move has to be the only correct move in the solution.
Good luck!
The purpose of taking a piece with restricted move possiblities but not in order to avoid stalemate?

Please, think of a reason verbally what the benefit should be. Why R/B instead of Q!?

My quick verdict: impossible
i have no idea on how to do this but maybe its possible if the underpromotion can prevent stalemate later (like 2 or 3 moves), or if the underpromotion (to a knight) can prevent ourselves from being in stalemate...
Underpromotion in a Knight is cut out I think. A knight fork is a simple reason without stalemate.

The Queen "consists" of Rook and Bishop. One usually underpromotes because otherwise the other add. function would deliver stalemate.

So how is this supposed to work without stalemate? Try to explain what you are trying to construct! TY
I believe the idea is that the piece can be taken by the opponent and we should find a position where the opponent would take the promoted queen but not the bishop or the rook, because it is better for him also to keep more pieces on the board in this case. Somehow it would lead to a bigger advantage to underpromote to a bishop or a rook (protected by one of our pieces) that our opponent would not take than a queen that he would take. Without any stalemate or checkmate involved.

I would be interested to see that but I am not sure it is possible.

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