The problem is caused by insufficient feedback. At low frequencies the feedback is fine, which is why they can play bass well. But as frequency is increased, the distortion goes up with it because the design lacks the Gain Bandwidth Product needed to support high levels of feedback at high frequencies. This results in harshness and brightness since that is how the ear perceives the higher ordered harmonics generated by the amp.
You can’t just add more feedback; you might exceed the phase margin of the amp, causing it to oscillate.
Its a compromise.
I have a lower powered Radio Shack amp that sounds fine as long as you don’t push it hard. It tends to make the 2nd harmonic as its primary distortion product and that masks a good deal of the higher orders. But at higher volume levels there isn’t enough lower ordered content to mask anymore- and so it gets harsh. But if I run speakers that have enough efficiency, the amp never gets to those volumes and it sounds fine.
Put another way, even though a lot of the amps mentioned so far can make quite a bit of power, matching the speaker to them (using an easier to drive speaker) is paramount to getting the most out of them.