I see the 598's have a frequency response of about 12 - 38500 whereas the FiiO has a frequency response of 20 - 20000.
Is that a bad thing? I don't want to buy headphones only to hamstring them with the DAC.
First off, your ears can't hear outside of 20hz to 20,000hz. Also, nearly every recorded material out there barring movie SFX like on The Conjuring and Paranormal Activity (which use infrasound) won't even go down to 20hz, and at the other end, it's not like you'll consistently listen to Sarah Brightman and Mariah Carey.
Second, the amp doesn't chop off everything outside of 20hz to 20,000hz. The amp manufacturer is just saying that effectively, "this is what matters as far as the signal it will get, this is where we measured." Because again, you won't be listening to infrasound. Even HT systems would do better with bass shakers on the seats rather than depending on the subwoofer to do all the infrasound.
Third, headphones list a range that is wider than 20hz to 20,000 for a variety of reasons. First is marketing, so as a buyer, you'd look at the specs and go, "wow this has a wider response!" but you're not looking at the actual graph, which is like this:
At 20hz, you're already -12dB relative to 1000hz and it just goes downhill from there. That's difficult to hear assuming your music has 20hz audio that is at the same average level as the frequencies covered by the vocals for example. The mic can't even pick anything up beyond a little bit past 20,000hz, and human ears at their best condition goes up just around the point where the HD598 trails off.
If anything, in some cases extended treble response
might indicate lower distortion in the high frequencies, but not really. Speakers using dome or cone tweeters are typically rated up to the mid-20,000 range, with a few exceptions, but you're more likely to find one that is just jagged in that region. Ditto headphones. This is mostly just marketing. Some planar and electrostats however are very smooth, but it's
not caused by the frequency response. Rather, the extreme treble response and the smoother curve are both products of the same attribute of such speakers: the way the driver vibrates rather than "pumps" the way dynamic drivers do is very conducive to low distortion reproduction of treble, since they don't move too much physically and can do the 10,000++ movements faster. At the other end however is how dynamic drivers can more efficiently produce low frequencies (even as they trail off more sharply at the very low bass range) thanks to how they pump, and they can go louder since they don't need to move as fast as when they have to produce high frequencies.
Just look at the things associated with low and high frequencies. The former is about "slam," more like swinging a hammer, the latter is associated with "sharp," so think of how a fencer can hit you several times in one go (or anime/video game samurai who can leave an opponent who looks like teppanyaki steak ready for plating; in reality a really good samurai will only need to land one critical hit, and probably didn't even need to draw his sword). Look at how an American V8's long stroke engines "pound" out a lot of torque and have a bassy sound, while a Ferrari (9,000rpm V8 or 8,000rpm V12) or Honda S2000 (9,000rpm I-4) or MVAgusta (15,000rpm I-4) or would have a higher frequency tone as it screams past you at the main straight (vs a Camaro at a stop light) as its shorter stroke allows for higher rpms (ie, cycles, as in hz). Hell, even a Ducati which uses a twin might sound more like a Corvette at a stoplight, but it will scream past you with a sound closer to a Lamborghini since by that point it's got the engine close to the 12,000rpm redline, which is much higher than any Harley.
