Show a logical sequence leading to a reversed scotch then.
Why does Reversed scotch not exist?
The only way i can imagine reversed scotch is actually a pretty known opening trap. Black will end up down a pawn if he attemts that.
However, if Black attemts reversed scotch this may happen.
Imagine this game:
1. e4 e5 2. Nf3 Nc6 3. h3(?) d5
In general, if white plays any nonsensical slow move on move 3, there's an opportunity.
The reason you don't have this is because beyond that of 1200-level knuckleheads that lack the common sense that traps are useless, nobody in their right mind would play 3.a3. Outside of some cheap tactic if Black were to play 3...d5, the move does nothing for White. 3.f4 fights for the center by attacking e5. 3.Bc4 develops another piece and attacks the weak f7-pawn. 3.g3 prepares to develop a piece on the long diagonal. 3.a3 does absolutely nothing for White's cause. All it does is make White HOPE that Black plays 3...d5. If Black does not play 3...d5, and instead develops a piece, like 3...Nc6 or 3...Be7, 3.a3 does nothing for White, and hence why it is not a recognized opening.
The only "traps" worth playing are ones that happen to occur through a legitimate opening. It is circumstantial. Not THE REASON for playing a move.
For example:
Here, we have a trap that is purely circumstantial, and really, White did it to himself. First off, 9.Bb2 is far stronger than 9.Be3, but here, there is a trap that I had an opponent fall for in an over the board tournament game on January 30, 2020 (right before COVID). He played 10.Nc3??, when 10...Nxe3 11.fxe3 Nxb4 wins for Black. But Black did not go out of his way to play something obscure to create this trap. It happens to occur in the main line. If White plays the best move, which one should always assume, Black is happen with his position. There is no let down.
After 1.e4 e5 2.Nc3 Nf6, there is nothing good about 3.a3. If Black doesn't fall for 3...d5, the move 3.a3 serves no purpose and wastes time. That is why the line above is a line of the French but your proposed line is NOT a reversed Scotch.
Now the fact that 6...Nh6 is under a cloud these days due to 8.Bxh6 instead of 8.cxd4 is a different matter all together, but this was not discovered until within the past few years. Most players with Black now play the old 6...c4 against 6.a3, or they will play 5...Bd7 (Euwe Variation) instead of 5...Qb6.
...nice essay?
Seriously, it shocked me you wrote that much, but definitely thanks for writing it.
I have written far longer responses than what I sent you here. I have written entire chess articles for a blog for over 3 years, and wrote maybe 5 or 6 articles for American Chess Magazine but quit that because the editor wanted me to write useless, meaningless fluff. I was writing about the history of openings, and he wanted games included, which I did. But then he wanted garbage added that is currently meaningless.
So I was able to write articles on some sound lines, like the Advance French and the involvement of players like Aron Nimzowitsch and the history of the blockade, with famous games like Nimzowitsch - Salve - 1911, along with a few more recent games. Worked out fine for the Marshall Gambit, Kings Indian Defense, Etc.
However, when trying to cover lines like the Portisch-Hook Variation of the French or the Vienna Game, the editor wanted useless fluff or wouldn't accept the truth, or even accept what I was specifically covering. The Portisch-Hook has the very specific idea of using the Queen to block the a-pawn from advancing, not allowing a4 and Ba3 by White, infiltrating on the dark squares. But because he didn't agree with the line, he tries to tell me that Portisch and Bill Hook were fakes, and that far earlier games involved 7.a4 Qa5, but that is NOT the same line, yet he was a stubborn bull and I said fine, scrap that.
I try to do specifically the Vienna Game. 1.e4 e5 2.Nc3 Nf6 and now 3.f4, 3.g3, and 3.Bc4. I specifically said I was covering 1.e4 e5 2.Nc3 Nf6. The history of THAT line/opening. No, you gotta throw in 2...Nc6 3.f4 and include these 3 games (all 3 were lines that are basically refuted today, but White won them back over 100 years ago).
I refused to include content that is totally refuted today. He went a few steps too far and I quit abruptly, but a few of my articles are in issues in the 20s.
So yeah, I can write a lot!
Imagine this game:
1. e4 e5 2. Nf3 Nc6 3. h3(?) d5
In general, if white plays any nonsensical slow move on move 3, there's an opportunity.
Not entirely because if you take with the pawn the only recapture black has with the queen while white always recaptures with the knight in the scotch. It'd be more like:
1. e4 e5 2. Nc3 Nf6 3. h3 d5
Realistically speaking 3. h3 would be a seemingly pointless move in the Vienna. 3. g3 is the current modern way to play the Vienna and in fact d5 is the current way to counter it.
But then the move g3 is never matched with a g6 in the regular Scotch, so no again, there's no real way to call something a reverse Scotch.
Seriously, why does a reversed scotch not exist? Or reversed versions of most over openings? There could EASILY be an opening called Four opposing knights game, Scotch variation.