Yes the 1/8, 1/10 output impedance is a rule of thumb. Yes over damping and under damping can be an issue and impact things like bass response.
As far as current delivery goes you're right... low impedance phones need less of a voltage swing and more current output. Or another way of looking at it is that you want an amp that has more peak current. So if you have transients and dynamics - drum hits, bass, etc. it will have more oomph and won't distort or clip or sound anemic. Some may not agree with me -- I think a lot of people get hung up on having all this power in their headphone amp -- like more than what is really needed. The headphone is only going to use what it needs. Any more and you're not even using it anyways. Who listens to audio at 110dB or 120dB?
I've read the same thing about high impedance cans as well.
Don't even get me started on amps that have too much gain... ie you can't get past 9 o'clock before it's too loud. Proper amp design would allow for the pot to be almost totally open let's say 2 or 3 o'clock... then you still have headroom on top of that. Of course there are a lot of factors like the output V of your source. I think amp manufacturers do this to appeal to the wide array of headphones out there and don't design around one headphone.
I'm not sure about noise and at what level to get rid of noise. I've just read and heard that you want the pot as open as possible.
