Just my opinion, but the difference between bass drivers and midrange/tweeter drivers FAR exceeds the difference between comparable amplifiers. Except of course for planar-magnetic’s, ESL’s, ribbons, etc. Different drivers made of different materials sound radically different from one another.
Amplifier designers have to make compromises in their amps: bigger output transformers in a tube amp produce better bass than does the same amp with smaller transformers. But smaller transformers produce better high frequencies (smaller ones create less saturation of the transformer core, a consequence of magnetic flux).
Of course the above pertains to only tube amps. But ALL amplifiers are designed with compromises made. Using different amps for different frequencies makes a lot of sense. Everyone with a subwoofer is already doing exactly that.