Are all amps being built wrong?

The power amplifiers that drive our loudspeakers are mostly built as a low impedance voltage source. They have always been ... but why?

Loudspeakers have a (greatly) varying impedance over the frequency range. A current drive amplifier would eliminate the issues that stem from this varying impedance, and at the same time make discussions about esoteric speaker cables that strive for optimal R, C, L superfluous. Although there still would be these un-measurable ’this (very expensive) cable sounds better’ debates and opinions ... and that’s OK, that’s part of the fun. :)

So ... why are amplifiers not built as a high impedance current source?

This is an interesting read:
The answer is economics. Amplifiers are voltage sources and practically all speakers are designed around being powered by a low impedance voltage source. Change the output impedance of an amplifier and then it sounds better with some speakers and worse with others. The industry is not going to get together and do an Avalon-Spectral-MIT marriage of specification. The ones making current source amplifiers are mostly the ones making active speakers. In short, to optimize a current source amp you must convince the speaker maker to tailor his specs to your amp. Not gonna happen. 
Audioman and andrewkelly I believe you are confusing voltage drive amps that have high current delivery capability with current drive amplifiers.The two types are more like opposites.The first type can drive low impedance loads and tend to have high damping factors and low output impedance whereas a current drive amplifier will suit higher impedance speakers [8-16 ohm] and will have a lowish damping factor and highish output impedance.
I have bakoon amps from Japan , they work on that principal , great amps . I have found my for ever amps.
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Bob Carver made amps under the Sunfire brand that had speaker outputs selectable for voltage or current drive. I’m told the current drive was created by the insertion of a series resistor.