Well, it is a bit more subtle than that, because you would not know what line B leads to without searching it first. And after you have done that, it is too late to prune it. So what really happens if that after you have found the single reply to the first move of line B that leaves you stuck with the doubled Pawns, you consider the first move of B refuted, and you prune the remaining replies to it.
But you are right in the sense that positional characteristics can also be sufficient reason to reject a move. This is purely a matter of evaluation, though. Whatever search method you would use, it should in the end give you the line to the position with the best evaluation that you can force (the 'principle variation'). If there is no mate in view the evaluation of positions must be based on heuristics. Piece values are one such heuristic. In general one should base the evaluation only on features that are not easily changed. Otherwise it would be pretty meaningless, as you know the game must go on from there (even though it is beyond your capability to take into account what will happen then), and if the feature would in general not persist after the next move it is pointless to optimize it. But next to material composition pawn structure is definitely a persistent feature (with FIDE or Shatranj Pawns!). King safety as well, when the King is a slowly moving piece.
What you will have to consider in evaluation can indeed depend very much on the rules of the variant. Using a neural network for evaluation (as both AlphaZero and NNUE do) and training that on positions from games is a method to avoid having to think about that yourself; you hope the NN is clever enough to recognize the important features, and quantify their importance. Whether this leads to different pruning in alpha-beta search is of no importance; this kind of pruning is guaranteed to have no effect on the principal variation that will be found. With or without pruning this would be the same. The pruning is just an optimization to get that same result, which was fully specified by the evaluation of the tree leaves, without wasting time on lines that neither of the players would want to play.
From conventional chess engines it is known that pawns on the forelast rank, and king safety can have values comparable to the material value of a minor.
Well, it is a bit more subtle than that, because you would not know what line B leads to without searching it first. And after you have done that, it is too late to prune it. So what really happens if that after you have found the single reply to the first move of line B that leaves you stuck with the doubled Pawns, you consider the first move of B refuted, and you prune the remaining replies to it.
But you are right in the sense that positional characteristics can also be sufficient reason to reject a move. This is purely a matter of evaluation, though. Whatever search method you would use, it should in the end give you the line to the position with the best evaluation that you can force (the 'principle variation'). If there is no mate in view the evaluation of positions must be based on heuristics. Piece values are one such heuristic. In general one should base the evaluation only on features that are not easily changed. Otherwise it would be pretty meaningless, as you know the game must go on from there (even though it is beyond your capability to take into account what will happen then), and if the feature would in general not persist after the next move it is pointless to optimize it. But next to material composition pawn structure is definitely a persistent feature (with FIDE or Shatranj Pawns!). King safety as well, when the King is a slowly moving piece.
What you will have to consider in evaluation can indeed depend very much on the rules of the variant. Using a neural network for evaluation (as both AlphaZero and NNUE do) and training that on positions from games is a method to avoid having to think about that yourself; you hope the NN is clever enough to recognize the important features, and quantify their importance. Whether this leads to different pruning in alpha-beta search is of no importance; this kind of pruning is guaranteed to have no effect on the principal variation that will be found. With or without pruning this would be the same. The pruning is just an optimization to get that same result, which was fully specified by the evaluation of the tree leaves, without wasting time on lines that neither of the players would want to play.
From conventional chess engines it is known that pawns on the forelast rank, and king safety can have values comparable to the material value of a minor.