Sure they affect the sound, but with modern instruments (say electric guitar) the amp is very much a PART of the instrument.
As an example you could say the spruce top of a classic violin gives it a "smooth" sound by attenuating the high frequencies. You could make the violin top out of high tensile steel and it would have "much better high frequency response" but then it would sound tinny, harsh etc. Having an instrument where all the frequencies are reproduced equally is NOT a guarantee it will sound better.