So, is there any reason that, at some point in the future, a $200 USB powered dad/amp couldn't sound as good as current $600 battery powered dad/amps. I have the impression that in the last 2 years the USB powered devices have improved quite a bit and perhaps it's reasonable to assume that they can keep on improving ..... at least for a while.
Audio is not moving very quickly. If you look at where most of the money and engineering talent goes, it's not there (and most of it into the chipmakers, people doing the mass-market stuff). Recent technological breakthroughs don't really have much impact on what you can do with regards to sound quality, so I wouldn't read too much into timeframes of a couple years as meaning much. If there are improvements in audiophile-centered products, which there are, it probably has to do with the designers themselves becoming more experienced as they ride the personal audio market. i.e. they're making do with the same kind of stuff that was already available by improving their techniques and somebody could have done the same years ago.
The very integrated audio electronics on a phone or most consumer-centric media players are heavily optimized for lower power consumption. You can get better audio performance (say better linearity, lower noise, though not necessarily by any level that's audible in most cases) going with a design with more discrete parts and/or higher power consumption.
For concert-level volumes on high-impedance headphones or very insensitive sets (i.e. for headphones only audiophiles use or possibly some in music production who would definitely not be driving this stuff off a mobile or USB-powered device), you'd need your own specialized design.
The battery-powered stuff is usually even more power-constrained than USB-powered DAC/amps. I mean, in the latter category you have the CEntrance DACport running a Class-A amp off of internally generated +/- 9 V rails. That would suck your battery dry in no time. On the flip side, a battery gives a very stable (on short time scales), relatively noiseless voltage supply. USB power is considerably dirtier. However, depending on the device and target power output levels, the voltages may need to be converted anyway, so what you get input may not be that relevant. And even if USB power is dirtier, you can use the higher power budget to filter it properly. The other thing to keep in mind is that a lot of carefully designed audio electronics are not very sensitive to power supply noise in the first place, so it could be a moot point.
Anyway, there are a lot of factors other than where the power is coming from. It's up to the designer to do things properly. (Of course, none of this makes as much of a difference as most audiophiles think, anyway, so take it as you will.)