Two players could start from any checkmate position ; the one player taking black , the other white, they could play chess backwards with the goal of trying to get all of ones pieces to their original positions first. Could there be a way to make this feasible?
This is just my opinion, as I doubt the question can be objectively answered, but I don't think this is feasible.
There are a few big problems arising from the idea of going backwards in the game of chess, and not only that the pawns' movement must be inverted, but also concerning the captured pieces. How to decide when a captured piece can "emerge" from the graveyard is, IMO, quite challenging. One can't simply set that every time an opponent's piece moves, you can put a captured piece on the square just left empty, since this would mean that a player has the right to "move" twice: to choose which piece to put on said position and then to move another (not necessarily different) piece. And this same problem applies to pawn promotion, when a player could choose to transform a piece on the last rank to a pawn on the seventh (or second). This doesn't happen in normal chess and I find it a little of an abomination.
Moreover, assuming all the pieces are already on the board, none of them can be captured (including the king, who now can enter into check but cannot be checked by an enemy piece). Plus, there are several strategies that any of the two players can adopt as to win almost immediately, one of them being to put a knight on the last rank, for example on a bishop's square. It would be impossible to a black piece to dislodge it, but if all the pawns are on their starting squares, the knight can go back to his place while the bishop can never trespass the pawn "chain".
This would lead to problems concerning what moves are legal and what are illegal. If, for example, we assume that a player must be capable of completing his objective, that is, any move that impedes the opposing player to complete his task is illegal (like forcing him to put first all the pawns on their squares but leave out the queen), would mean that one can enter a never-ending discussion of when a knight shall leave the last rank (the pawn has to be two squares advanced, or one, but what if the knight has all the other exits blocked and can no longer move, is it illegal to move the pawn thus A wins or the knight is in an illegal position thus B wins...). Or maybe we shall decide that if a player cannot attain his objective, he directly loses.
Well, I have to accept that maybe it is plausible to make such a game, but that would not resemble much the chess rules, and they would be so complicated that I don't think the game could be playable.