I played the opening long enough to understand that 6...Bxc3+ gives nothing. I know that the Budapest is for romantic souls but i didn't knew that serves and illusionist like you. The double c pawns is not a weakness for white and black has absolutelly no plan to create considerable counterplay. Perhaps instead of wards you want to show something from your rich experience that everyone on this planet missed!?
I read Moskalenko's book and i don't see nowhere a concrete plan for black after 6...Bxc3+ or 7...Bxc3+. In order to sell the book more he didn't mention not even one from Gligoric games in the Budapest Rubinstein variation. Anti-selling example.
Doubled isolated c-pawns and an isolated a-pawn aren't weakness for White? Um, ok. I suppose the correct way is to take on c3 without wrecking White's pawns as you showed in your diagram, that makes perfect sense.
BxNc3+ is a very basic and key move for Black in that line. If you don't grasp why that move is good you have no business even studying openings, you need to go read "Basic Strategy for Beginners" before you run your mouth off about anything, much less an opening you don't even play. (Oh but you used to play it, and gave up on it before you learned it past move 5, I know this makes you an expert about it.)
And apparently you didn't read Moskalenko's book as you claim (or else you have zero reading comprehension) because he shows lots of ideas, in particular, the Schlechter Knight manuever of Nf6 to e4 to c5 blockading the isolated doubled pawns. This is elementary strategy straight out of My System. Meanwhile White's queen is exposed in the center, Black has a lead in development, semi-open e and f files, and the knight on c6 can hop to e5 creating what Taylor referred to in his book as "Schlechter's double-fisted knight blockade", all this ON TOP of the shattered White queenside and weaknesses to work with adds up to considerable counterplay. This is the price White pays for keeping the extra pawn and why lots of players prefer Nbd2.
My dear flying Dolphin! Please stay in the water and stop imagine sharks with out jews and teethes. The 6...Bxc3 line was considered the best approach for a long time but game after game lost it value to give black a considerable game plan to play for something more. If you watch any kind of serious Data you will notice that 6...Qe7 takes more and more preferences last years. Remember that you don't play the Budapest gambit to enter in to a drawish position, it supposed to fight for the unexpected. The " Schlechter knight " it's not something that can frighten white more than confuse black it self. The theory story with the double weaken c pawns and the twin knights no longer being attractive! We are in 2015. Nimzowitch time has pass! We live on the Jobava's twilight. Let's talk practical.
I won't go into detail since his discussion of the line is probably the most valuable part of Taylor's book. But his analysis of the various "f4" games in a certain line has the pedigree of World Champions and gives White a really nice edge. I've won a few cc games using his recommendation in his book designed for Black!
By the pedigree of World Champions do you just mean there are the two games Spassky vs Illescas and Smyslov vs Blasec? In both these games Black made opening inaccuracies. In Smyslov vs Blasec, White played 6.Nc3 and instead of castling Black immediately took the pawn back, which allows the f4 attack with an extra tempo for White since he hasn't developed his light squared bishop yet. Though I've done some analysis and found that even here with the extra tempo the f4 attack gives White no advantage and the position after f4 is equal. Black has to know what they're doing and even put their king on d8 if necessary, if they decide to take the pawn back immediately after 6.Nc3 instead of 0-0. The point is Blasek didn't have to allow that in the first place so this game doesn't say anything objective about the merit's of an early f4. In Spassky vs Illescas, Illescas had equality. All he had to do is play normally with 10...d6 after Spassky went Kh1 instead of trying to force through the Drimer rook lift with 10...a5 and on 11.f4 go Nd7, with the idea Nf6 (controls e4 and all f4 has given White is a backwards e-pawn on a semi-open file) I believe also that 13...h6 was a mistake, preferable was g6 with an idea of f5 to blockade f4. Getting f5 in and blockading in this way is one of the few basic defensive ideas Black has to know. Objectively the attack isn't fearsome, because look, White hasn't developed their queenside, the bishop is still on c1 staring at a wall of pawns and blocking in the rook. As Steinitz said an attack can only succeed if it deserves to. This quick hack-attack White launches before they've completed their development doesn't deserve to succeed, and can only work if Black makes mistakes.