I also have this question.
I used
https://www.headphonesty.com/headphone-power-calculator/. I do see the power calculator showing that phones or laptops aren't recommended. Based on that, an o2 amp should be enough to drive a hifiman he-560 (7.27 VOLTS RMS) at 110 DBSPL. Would this actually lead to any clipping or uncontrolled bass?
At 7.2V the HE560 reaches 116dB peak (about 100dB average).
Above that there will be clipping. No idea where the 'uncontrolled bass' comes from. I reckon its another way of saying they hear distortion (clipping)
I also understand that better SNR means that when I increase the volume, there is less distortion so that plays a big factor.
SNR and distortion levels are not really related. One can have a high S/N ratio and no distortion and have an amp with loads of distortion but a very low SNR.
Just like the OP, I will like to know if it is myth that a more "powerful" amp (lets say 3.5 watts at 50 ohms with similar SNR) will make the sound "better".
An amp does not provide or push 'power'. It provides a voltage and depending on the headphone's impedance a current s drawn (and thus power).
A powerful amp will not clip, a whimpy amp will. Whimpy amp may sound poor when maximum output voltage or current is reached.
If i can play the less powerful o2 amp to the same volume with volume knob adjustment and human hearing cannot hear the increased SNR, will the bass become less controlled based on the numbers (doesn't clip but maybe distortion?)?
I also don't understand why ppl say that more powerful amps make the midrange better (more detailed, fuller, etc). If headphone power calculator show that the o2 drives the inefficient he560 planar, then why would the midrange sound sonicly different from a more powerful amp?
The S/N ration doesn't have anything to do with this. As long as you do not clip the O2 it can not be distinguished from a more powerful amp at the exact same volume. Regardless what the opinion on the interwebs is.
However, I do have to say that I do hear a difference between a more powerful amp compared to an o2. But that is from a limited listening and there might be subjective bias. That is why I am trying to get to the root of this objectively.
Only controlled and level matched blind tests (properly conducted) will tell you.
Any sighted (knowing what you are listening to) will lead to incorrect assesment.
I know there are a lot of factors that come into play. Like OP, I feel like a lot of people that have a much better technical understanding don't clearly come out to say whether "more power = better sound" is a myth.
It is not a myth when the less powerful amp is clipping or when there are other factors at play.
I am giving a clear test case (he-560 and o2 amp compared to he-560 with 3.5w at 50 ohms amp). Does more power in this case equal better sound?
Only when you reach clipping levels on the O2.
BTW, I know JDS atom is the better amp to buy than the o2 but the headphone-power-calculator site didn't have jds atom as an option. It seems like JDS atom is pretty much end game amp for precise reproduction of sound. What headphones will need more power than JDS atom can produce at normal listening volume?
Atom can play 1.5dB louder than O2 (on mains)
In normal to loud circumstances they are indistinguishable.
O2 can be used on batteries and is metal, Atom only on mains and is plastic. Pick your poison