@jyrki,
You are right that 2.c8=Q will likely win. But that line is a full pawn worse that the solution. Instead of a full exchange, white is only up an exchange-for-a-pawn, which is typically not an ALT.
And that extra pawn in the solution is on the penultimate rank. So with some good advanced pawn tactics, black will lose a bishop taking the promoted pawn. So the variation you cite is really a piece worse than the solution.
On move 2, many moves are very favorable, up an exchange for a pawn, which is likely winning. Stockfish16, playing perfectly for 30 ply and beyond in a long endgame, predicts a +4 eval. But the material balance is not good enough for an ALT per CT's traditional assessment. FAQs warn about depending on long endgames to achieve a clearly winning advantage. Tactics training is about finding short term material gains.
[FEN "2b5/1rP1kppp/3rp3/p1N5/8/6P1/Pn3P1P/1RR3K1 w - - 0 1"]1.Nxb7 Bxb7 2.Rxb2 { Correct, up a full exchange. }
[FEN "2b5/1rP1kppp/3rp3/p1N5/8/6P1/Pn3P1P/1RR3K1 w - - 0 1"]1.Nxb7 Bxb7 2.c8=Q { !? non-ALT with an eval that keeps increasing with depth, reaching +4.03 at depth29 with Stockfish16 } Bxc8 3.Rxc8
@jyrki, What are your thoughts about the threshold CT has historically used? Should problems like this be disabled? Why?
Side point:
The problem cannot continue beyond move 2 because in the solution variation, many moves by white are completely winning. The advantage is not just an exchange, it is a very robust, error-tolerant +4.5 eval with many winning continuations.
@richard,
The counterargument is that SF reaches a +3.9 eval for 2.c8=Q at depth of only 20, and this is, as @jyrki points out, almost equal in eval to the 4.5 of the solution.
Is that too close to be a valid problem? Toga's eval for 2.c8=Q is +1.28/depth17 partly because move 4 is suboptimal.
This is a 1132 standard, 1457 blitz rated problem. OTB, the 2500-rated white played the solution 2.Rxb2 and maintained the promotion threat to strategically win the game. But Stockfish16 at depth18 has 2.Rxb2 as +4.16 and 2.c8=Q as 3.80. It is not ideal to have a nonALT dominant error with a +3.80 eval that is only 0.36 less than the solution.
[FEN "2b5/1rP1kppp/3rp3/p1N5/8/6P1/Pn3P1P/1RR3K1 w - - 0 1"]1.Nxb7 Bxb7 2.c8=Q { !? harsh non-ALT } Bxc8 3.Rxc8 { up only exchange for pawn } Rd2 4.Ra8 { Toga's weaker choice } ( 4.Rbc1 { Stockfish16 better choice, eval 3.69/depth20 } Rd5 5.R1c7+ Kd6 6.Rxf7 Rd1+ 7.Kg2 Nd3 8.Rxg7 Rd2 9.Re8 Kc6 10.Rf8 Rxa2 11.Rxh7 { up an exchange and a pawn } ) a4 5.Ra7+ Kf6 6.Rc1 Nd3 7.Rcc7 Rxa2 8.Rxf7+ Ke5 9.Ra5+ Kd6 10.Rxg7 Nxf2 11.Rxh7