This much better signal to noise ratio of my class D amp makes it sound much cleaner and with less grain. Highs sound smoother on it because of that.
Thin? Well, if you get the right gear to feed it (AC Power, DAC, correct digital signal processing, neutral to warm preamp, etc) you can get a very detailed sound, with amazing soundstage and dynamics, with out losing smoothness, body and tone, at all.
Im sure you can get good sound with class A amp, but you also can do it with a good class D amp, at better price in most cases. Also lighter in weight, cooler at running temperature and with less energy consumption.