Harm: If there is a best strategy (i.e. best set of piece values) it must be shared by both sides. The theoretically best play is amongst the set of self-play games. And it is only the score that results from theoretically best play that determines the piece value.
First there is no 'best play' without having complete information. But such is far away from human experiences. Nevertheless supposing to be in such a hypothetic well informed situation, indeed participating optimal players would behave related to the way you stated - beside of the fact, that then there would be no longer a need for any piece value at all, because then all nodes merely will be valued as +1, 0 or -1.
So the question is, whether your approach would be convergent to any claimed ideal value model. Living within a world without such a perfect information and using engines, which all are wearing blinkers then hiding tabooed piece trades, I intensively doubt on that. You will have to try a lot of different models implemented into engines of equal maturity to find out after a lot of experiments.
First there is no 'best play' without having complete information. But such is far away from human experiences. Nevertheless supposing to be in such a hypothetic well informed situation, indeed participating optimal players would behave related to the way you stated - beside of the fact, that then there would be no longer a need for any piece value at all, because then all nodes merely will be valued as +1, 0 or -1.
So the question is, whether your approach would be convergent to any claimed ideal value model. Living within a world without such a perfect information and using engines, which all are wearing blinkers then hiding tabooed piece trades, I intensively doubt on that. You will have to try a lot of different models implemented into engines of equal maturity to find out after a lot of experiments.