Right, I forgot about the rook. I was looking at the wrong diagram without it, LOL
tsume shogi time

There are plenty of tsume problems where the defense making drops is correct for whatever reason. Just not these simple problems.

Well, I think it is good to see it out fully. I just made a quick glance and messed up now. Had I spent more time looking and fully thought it out I would see that keeping the bishop is best.
Even if you don't actually make the move or see a drop, you still should realize it is the only thing a player can do.
To say delaying it is a waste means you got to the stage where you considered it.

If the only thing you can do is make pointless drops, the correct thing to do is resign. Japanese shogi culture is a big part of it.
At the beginning of a game, you say "yoroshiku onegaishimasu". This translates to:
"Hello. I hope we have a good game. I will play honorably and fairly, and I hope that you will do likewise. I will respect your skill as a shogi player."
Respect means that the losing player resigns, when it's clear they have lost. In professional shogi, this can mean a mate-in-17, or just that they will get eventually mated since their king is exposed and they have no attack. Personally, I will concede around mate-in-9 against an equal opponent.

I understand resigning in a game. I think we are getting too critical. I am just speaking in terms of online training. Play it out to make sure you understand it fully. As you can see above I didn't do it.
Even if dropping pieces was not supposed to be used in solving tsume problems, then the solution has two answers still. The rook could move down a square in the OP puzzle and promote to a dragon. It doesn't have to go sideways to the left.
No. R-23+ Rx33 and the horse is gone. No mate. Only the solution R-32+ is correct.