I've owned the Asgard 2 along with matching Bifrost AKM 4490.
I've use it always in low gain with my former AKG K702.
In low gain the mentioned setup maxed at 145mW into 62 Ohm
I've never had to max out the volume, far from that indeed
Basically at the same level as ~60mW into the HD600.
For most applications and listening levels, including loud (and not 100% healthy) listening levels you need 50mW for K702.
Power is vastly overrated. The quality of the amplifier on the other hand is the real thing and can have a very important impact on sound quality.
Well it's not like I'm going for all out power either at the cost of THD+N, or going all out on power and low THD+N on something like the Lyr.
The idea still is that an amp with slightly more power (note that slight here isn't "a few mW's over" since every +3dB needs roughly double the power input), properly designed, would have less distortion and noise, hence going for something like the Asgard or Magni, without pushing the design that it starts to get higher THD or you get crossover distortion. Of course if you can get something that would basically be the First Watt for headphone amps - pure class A, ~75mW at 300ohms and ~200mW at 32ohms, very low noise, etc - then that also works. But as it is for $250 you can get pretty much inaudible noise and distortion on the Asgard anyway. I have the HD330 which has roughly the same (if not lower, since it's measured at 1000hz or so, where it has a slight boost) sensitivity as the K7xx series at 93dB/1mW, and yes, it
can get very loud on a Xonar U3, but that doesn't mean it sounds good. I have a Meier amp that does way better, and yes, that's due a lot more to the low distortion and noise, but given the price of amps that can drive practically anything without getting offset with high THD+N nowadays, it's not like you're basically doing what made the First Watt necessary, ie, most amps sacrificing distortion and noise performance for watts.
OP was also using a soundcard, and it couldn't get loud enough for him. That's not a function of distortion (ie the quality of the circuit, including output impedance), and unless it was one of the USB-powered ones, these soundcards otherwise have a lot of power too, and not just from people misinterpreting fancy names for High Gain like "Extreme Pro Gamer Mode >150ohms" as an indicator for power output.