I am not convinced. 'Concentration' of attacks is certainly good, but I always thought this would be defined in terms of orthogonally adjacent attacked squares. The attacks of the Wazir are diagonally adjacent, and there is no special reason to think that is useful. With orthogonally adjacent attacks you can attack a Pawn and the square it could move to, so it cannot escape.
I see one advantage of a piece with W capture, though: if it is in time to stop a passer from promoting, it can annihilate the passer by attacking it from the front, thus blocking the square it could escape to rather than attacking that. In test on large boards (like 12x12) I discovered that it was very hard to compensate the R-B imbalance with Pawns. No matter how many extra Pawns the Bishop side got, he kept losing by about the same amount. I ascribed that to the ability of the Rook to annihilate isolated passers, while the Bishop can only prevent their advance (and then remains bound to stopping that passer forever). With so many Pawn on the large board most end-games started with scattered isolated Pawns, and the Rook would always win those end-games against Bishop or Knight. The extra Pawns were just cannon fodder.
As for mKcB and mKcR versus mKcN: the latter could be much weaker because it is slow, and cannot catch up with passers. But for mKcR it is enough that it can get behind the passer on the same file to stop it from promoting. And mKcB can advance its attack on the Pawn file by two squares per move by moving diagonally.
I once tested mKcN and mNcK. The former was about the same value as N and K. But the latter was about half a Pawn stronger! This surprised me, but then I realized it had the best of both worlds: it has the larger speed of the Knight, and the concentrated attacking power of the King, and thus the ability to annihilate Pawns once it catches up with those.
I am not convinced. 'Concentration' of attacks is certainly good, but I always thought this would be defined in terms of orthogonally adjacent attacked squares. The attacks of the Wazir are diagonally adjacent, and there is no special reason to think that is useful. With orthogonally adjacent attacks you can attack a Pawn and the square it could move to, so it cannot escape.
I see one advantage of a piece with W capture, though: if it is in time to stop a passer from promoting, it can annihilate the passer by attacking it from the front, thus blocking the square it could escape to rather than attacking that. In test on large boards (like 12x12) I discovered that it was very hard to compensate the R-B imbalance with Pawns. No matter how many extra Pawns the Bishop side got, he kept losing by about the same amount. I ascribed that to the ability of the Rook to annihilate isolated passers, while the Bishop can only prevent their advance (and then remains bound to stopping that passer forever). With so many Pawn on the large board most end-games started with scattered isolated Pawns, and the Rook would always win those end-games against Bishop or Knight. The extra Pawns were just cannon fodder.
As for mKcB and mKcR versus mKcN: the latter could be much weaker because it is slow, and cannot catch up with passers. But for mKcR it is enough that it can get behind the passer on the same file to stop it from promoting. And mKcB can advance its attack on the Pawn file by two squares per move by moving diagonally.
I once tested mKcN and mNcK. The former was about the same value as N and K. But the latter was about half a Pawn stronger! This surprised me, but then I realized it had the best of both worlds: it has the larger speed of the Knight, and the concentrated attacking power of the King, and thus the ability to annihilate Pawns once it catches up with those.