If you get rid of distortion and phase shift across all frequencies,
will all amps sound the same? Should they? Even with different
topologies, parts? No more house sounds?
If their output impedance is also the same then at that point, yes, they will all sound the same assuming their power supplies are up to the task.
I would not characterize doing this as a mathematical extreme. Its simply what you do if you want to get it right.
The key is getting enough feedback and at that point it won't matter if its tube, solid state or class D. This is almost impossible with tubes as there are usually too many frequency poles resulting in a low 'Phase Margin'. If the phase margin of any amp is exceeded when feedback is applied, the amp will go into oscillation. This is one reason why tube amps tend to have less feedback than solid state, the other being that they are also inherently more linear and don't need that much feedback to have acceptable distortion figures.
Designers who have been up to the task of installing enough feedback in traditional solid state designs are rare. But it appears that the Benchmark and the Soulution are two amps where this is exactly what has been done.
In class D this is possible though a different means which is to add so much feedback that the phase margin of the amp is exceeded, causing it to oscillate. The oscillation is then used as the switching frequency. Such amps can employ quite a bit of feedback and the sound of them is really all about how well the power supply is built.
