SE class A amps don't have as controlled bass response as a push/pull design. I've noticed the bass to be very good with the Aleph, but if you are looking for extremely tight "robotic" bass, a SE design probably won't be to your liking.
They tend to be low on power output (rated watts) so if you are using a very difficult load and want to fill a large room with high spl, it's not going to happen. For most everyday types of speakers in small to medium rooms, the Aleph, as an example has no issues. Put a large pair of Maggies in a large room on the Aleph and try to reach a higher spl, forget it.
They run very hot and consume a fair amount of energy just sitting there.
Expensive hardware if done correctly.
P.s. you can buy high power single ended class A amps, but they cost a fortune, weigh a ton and put out a lot of heat and use a lot of electricity.