Nobody should listen to any music with anything but as flat a response as possible. Exaggerating bass is also terrible.
Now consider that most of this music was probably played in the crappy 1084 monitor speakers, so there's a lot to be said about listening to the Amiga in a hi-fi setting, it's just not what a lot people are used to. Add to this the fact of different filters on different Amiga models, and you have some standardization issues. The Sound Enhancer you didn't like, probably was made to compensate for the always-on high pass filter the A500 has. An unmodified A600 will also benefit from a bump on higher frequencies. An A1200 doesn't need such a thing.
Also in your later case, you are probably also hearing a lot of shitty MP4 artifaction, you say yourself they are low-bit, this will include lots of garbage. So why do you do this to yourself?
The Amiga itself doesn't have that much noise unless you are on a silent part and you are extremely anal. The music I put in my Youtube channel, which I master, is put through a gate so most of this shit isn't heard.