Why a queen instead of a bishop?

The problem is beautiful but wQ’s power is outrageous.
A true master of puzzles hides his idea optimally by making it original and unexpected.
The “tempting” moves which are not thematically related to the solution only detract a solver to waste his time. At least in principle, such a way of making a puzzle harder, is using a “crutch” to support a “lame” idea.
There’s anything but artistry in such crutch.

Here, the author’s idea would be optimally hidden with wB instead of wQ.
(I would perhaps prefere h#2* with bS on d1 instead on e4.)

However, in the original, among the cooks&duals, a solver might notice a 3rd thematic possibility, in case of h#2, which would justify wQ, e.g.:
1.Sxf6=wS(wQb3) a3=bP 2.Kxb1(bBb2) Bxa3=bB(bPa1=bB)#
(wRc3 prevents 3.Ba1xf6=wB(wSb2))

This thematic possibility alone, could be more economically shown:
White Pa2 Qe2 Bb1; Black Sc3 Kc1; h#2

Since there is wQ on the board, some other temptations might at least inspire a solver for composing:
White Qh8 Rc3 Pa2 Pe2; Black Sa4 Kb2; h#2
or
White Qb3 Pa2 Bb1; Black Pf7 Pe6 Ka1; h#2, 2 sol.

So, wQ offers some benefits for imagination 🙂

Peter, I’m not a perfect English-speaker, so I have looked for a word with two main meanings, something like both excessive & disrespectful.
If “outrageous” is not a proper word, that’s my fault and I’m sorry for misunderstanding.

wQ’s power is excessive and that shows a disrespect with regards to the content of (your own) solution. And in principle, I see it eventually as a disrespect for a solver, since the idea is not only well hidden by its own merits, but is also crudely buried under the numerous irrelevant wQ’s “temptations”.

So, I’ve been wasting my time on the “tempting Queen”, revealing absolutely nothing about the solution. wB would immediately make me solve what is there to be solved, instead of “solving” what doesn’t exist (as a relevant content).
The beauty of the relevant content was thus actually spoiled by exploring the irrelevant bluff.
Next time I’ll prevent it, I’ll first read the solution to see what is relevant.

However, I have to admit that my time was not completely wasted. At least, I’ve found some interesting attempts with wQ.
The examples I gave are just the redacted attempts which I had “imagined” during the solving. My “hopes” were in the white promotions, to “activate” Isardam.

Here’s another “redaction” of an attempt which I explored after abandoning the significance of wQ:
White Bf7 Rc4 Pa3 Bc1; Black Pe5 Pa4 Ka2; h#1.5, 2 sol.

1…Rc4*a4=b[+bPb3].. etc. is of course just a nice cook, but the other solution shows what I was indeed thinking about while solving your problem.

(It is instantly obvious that Isardam might have effect only in case of some SuperCirce promotion.)

In my example (W: Qb3,Pa2,Bb1; B: Pf7,Pe6,Ka1), 1.Ka1*b1[+wBb2]..etc. is a cook, created by the computer, not by me. The other solution was my idea, featuring the try 1.f7-f6=wP? which fails due to the changed color of Pf6 3.Qf8xf6=wQ(wP~)

It’s pretty clear that it’s comes from solving your problem, an attempt to use wQ to activate Isardam, for instance:
1…Qf6-e6=bQ 2.Qxa2=wQ(Pa8=wQ) Qxe4=bQ(bSa3/a4), but 3.Qxb1=wQ(wB~)!

Your suggestion about bPa3 is not clear to me. This would only give the additional reason for the capture, the line-clearance. Captures on e6/f7 are motivated exclusively by the arrival of these Pawns. bPa3 must be captured for opening the a-file, to legalize 2.bQxa2 in both solutions.

Well, this would better hide the idea, since 2.bQxa2=wQ seems impossible. You surely have a better feeling for the puzzle-subtleties.
But, when that idea (2.bQxa2=wQ) eventually comes to a solver, he knows that bPa3 must be gone, before asking himself about a possible purpose of bP’s arrival.

Without bPa3, 2.bQxa2=wQ(Pa8=wQ) is a legal possibility from the beginning, so the captures of bPe6/f7 are independently motivated. These captures make sens only after comprehending their pure purposes.

IMO, if your goal is to maximize solving difficulty, you should publish your problem in a magazine that has solvers, and not in an online magazine that prints the solutions next to the diagram.