Current, voltage, and power are directly related. They have everything to do with volume, and nothing to do with bass coloration and sound stage. The HD650, by the way, needs very little current and power thanks to its 300 ohm impedance and fairly high sensitivity. What it needs is voltage.
I can walk through a couple calculations if you like, to show you how much current and power it actually needs to reach high volume (I like to use 110 dB for that).
I would agree on some point. On calculation that seems to be very true but in the end it's the circuit and components' job to deliver the actual sound. For things to perform ideally we need quality caps, transformer, circuit etc. A budget cut in cost would definitely diminish the performance in some way. I am lying to you if I claim a $5 steak taste the same or even close to a lovely prime rib.
On the other hand, I must emphasize that one must listen to the actual sound and if possible, investigate the interior built of the DAC/Amp. Pay more and pay smart when investing in this accursed hobby.
It depends, All props color the sound in some way, some swore with neutral and some embrace colored interpretation (like tubes). As long as one enjoy and know what he is doing I think that's fine. For pros as long as they know their system well and how their hard work would be translated into other systems, that's also fine.