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'Because of all this, I suggest evaluating entire configuration of
pieces,
rather than a single piece.'

This is exactly what Chess engines do. But it is a subject that transcends
piece values. Material evaluation is supposed to answer the question:
'what combination of pieces would you rather have, without knowing where
they stand on the board'. Piece values are an attempt to approximate the
material evaluation as a simple sum of the value of the individual pieces,
making up the army.

It turns out that material evaluation is by far the largest component of
the total evaluation of a Chess position. And this material evaluation
again can be closely approximated by a sum of piece values. The most
well-known exception is the Bishop pair: having two Bishops is worth about
half a Pawn more than double the value of a single Bishop. Other
non-additive terms are those that make the Bishop and Rook value dependent
on the number of Pawns present. To account for such effects some engines
(e.g. Rybka) have tabulated the total value of all possible combinations
of material (ignoring promotions) in a 'material table'. Such tables can
then also account for the material component of the evaluation that gives
the deviation from the sum of piece values due to cooperative effects
between the various pieces.

Useful as this may be, it remains true that piece values are by far the
largest contribution to the total evaluation. The only positional terms
that can compete with it are passed pawns (a Pawn on 7th rank is worth
nearly 2.5 normal Pawns) and King Safety (having a completely exposed King
in the middle game, when the opponent still has a Queen or similar
super-piece, can be worth nearly a Rook).