Hans,

Indeed, your argument fails to take account of this gap between theory and
reality. People have not explored a significant fraction of the game tree
of Chess from the opening, or even from late middle-game psitions. And
computers cannot do it either. Nor will they ever, for the lifetime of our
Universe.

Outcomes that are in principle determined, but by factors that we cannot
control or cannot know, are logically equivalent to random quantities.
That holds for throwing dice, generating pseudo-random numbers through the
Mersenne Twister algorithm, and Chess alike. So Chess players, be they
Humans or Computers, will have to base their decisions on GUESSED
evaluations of teh positions that are in their search tree. And the nature
of guessing is that there is a finite PROBABILITY that you can be wrong.

Chess is a chaotic system, and a innocuous difference between two
apparently completely similar positions, like displacing a Pawn ofr a King
by one square, ort even who has the move, can make the difference between
win and loss. The art of evaluation of game positions is to make the
guesses as educated as possible. 

By introducing game concepts you can pay attention to ('evaluation
terms') one can classify positions, but the number of positions will
always be astronomical compared to the number of classes we have: even if
we would consider the collection of all positions that have the same
material, the same Pawn structure, the same King safety, the same
mobility, etc., we are still dealing with zillions of positions. And
unless material is very extreme (like KQQK), some of these will be won,
some drawn, some lost. The moment this would change (e.g. because we can
play from 32-men tablebases) Chess would cease to become an interesting
game. But until then, any evaluation of a position is probabilistic. The
game will most often be won for the player that goes for the positions
that offer the best prospects. The player that only moves to positions
that are 100% certain wins, will forfeit all games on time...

Now piece values are the largest explaining factor of evaluation scores,
if you would do a mathematical 'principal component anlysis' of the game
result as a function of the individual evaluation terms. That is a property
of the game, and independent of the nature of the player. Humans and
computers have to use the same piece values if they want to play
optimally. Only when the search would extend to checkmate in every branch,
(possibly via a two-directional search, starting from opening and
checkmate, meeting in the middle as tablebase hits) evaluation would no
longer be necessary, and piece values would no longer be needed.