> To follow on though, shoukdn't it technically be the case that piece values should in theory fluctuate based on current situation.
Yes. One common example is knights and bishops. Both are worth about 3 pawns, but knights are generally more useful in closed positions due to their ability to jump over pieces, while bishops are better in open positions since they can more attack and move long distances.
So in some sense, and I'm just brain-farting here, the value of a piece is a weighted sum of all the possible squares it could occupy during move generation. Something like a rudimentary path trace.
Now trying my best not to get distracted building chess machines. :/
Yes. One common example is knights and bishops. Both are worth about 3 pawns, but knights are generally more useful in closed positions due to their ability to jump over pieces, while bishops are better in open positions since they can more attack and move long distances.