I should get a chance to audition the HD800 this week. the thing about amps and dacs I mean a dac's job is to turn 1s and 0s into a wave form, and the odac does that as good as any other dac can if not better. So if you hear a difference in a 2 thousand dollar dac, that means that dac is messing the 1s and 0s and changing the sound, which is opposite of hifi, so it may or may not sound better, but technically speaking it is not doing a good job on what a dac is supposed to do.
Same with amps - an amps job is to deliver power to drive the headphones - an o2 at 6x gain has more than enough power to drive virtually any pair of headphones with minimum THD, so if a 2 thousand dollar amp sounds different, then it's messing with the signal to give an illusion of improvemen (which is not worth 2 thousand dollars imo)
That being said I do enjoy my OTL tube amp with vintage mullard tubes with my 650hd because I like how it Physically changed the sound to be more soft and pleasurable - but if i spend 1000-1600$ on headphones, i don't like the idea of also having to spend 3000$ on a dac/amp just to fix the headphones, because if it doesn't sound good on the o2odac, then thats mostly on the headphones. But i am hoping the hd800 will be enjoyable with my tubes.
you're focusing on the digital part of the acronym DAC. There's also the analog part, ie how well the DAC outputs an analog signal. Also, DACs have to make a lot of choices in how they "fill in the gaps" of the digital signal. the digital information is binary, and an analog system is continuous. DACs will differently make choices on how to make that conversion from analog to digital.
You're describing a DAC like it only passes along the digital signal. It CONVERTS a digital signal to an analog signal, and in so doing makes a lot of "choices" based on its design, for what that digital signal means in the analog realm. The analog realm imparts exponentially more information than the digital realm (even at the highest bit rates, continuous is always more information than binary). Because you're going from less information to more information, a lot of that information has to be "made up" by the converting device. A chord unit, for example will assume the smoothest possible transition between those digital points of reference, whereas a SABRE DAC will tend to have straighter transitions (that's obviously a drastic oversimplification, but it's just meant to illustrate a relatively simple point).
You're also wildly oversimplifying what amps do. Most even decent amps have a flat frequency response. The issue with amps has more to do with how the THD breaks down. Some amps will have low THD, but almost all of it is in the highest order harmonics. This doesn't strictly speaking change the frequency response, but it will result in the amp sounding harsher than an amp with the same amount of THD, but with the THD focused on lower order harmonics. The great sham of the O2 (and I say that liking the O2 and what it represents) is that it in calling it objective it pretended that all harmonic distortion was the same. It's been known for decades in speaker hi-fi that the breakdown of harmonic distortion is as important (if not more so) than how much total harmonic distortion there is.
Next, while most amps have plenty of gain, many don't have a stable enough power supply to smoothly impart that gain in a consistent way. Power can sag, interference can seep in, they can be infected with DC power in an AC circuit. A good, beefy power supply will cure those ills (the O2 doesn't have a very good power supply, except the battery units, which sound better, because they're on relatively pure DC).
Gain is only half the picture as well, in that an amp can have plenty of gain, but run out of voltage or current. This happens to people using the HE6 with an inferior amp all the time. Especially when combined with a poor power supply that means the amp can't even provide all the power it's supposed to have in the first place in transients.
Finally amps can differ in the amount of electronic damping they have available. This isn't an issue with the O2, but it is with a lot of otherwise good amps on low impedance headphones. You can debate how important this is (me and MeX3 have debated this a lot of times, but it is at least theoretically an issue.
When I'm buying an amp, gain is probably the very last thing I look at, as there only a handful of amps I've ever seen that don't have enough gain for my most difficult to drive headphone (the HD800 when equalized). This first thing I look into is the power supply. How stable is it? Then I look at the output impedance. Even for my high impedance headphones, I like the increased diaphragm control of a zero impedance amp. Some people however like the "fullness" of an amp with less electronic damping though. A matter of preference there I suppose. Next I look at what the total harmonic distortion is, and how it breaks down. These numbers are often hard to find published anywhere, but once you know what to listen for are pretty easily discernible. This is often what I think most Head-Fiers mean by "tube warmth" or "harshness" in an amp. It doesn't actually change the frequency response (contrary to the way most head-fiers talk about tube warmth, it doesn't actually add bass or roll off treble in a frequency response sort of way normally). My personal ideal amp is an amp with very low total THD, but whose THD profile concentrates half of all the THD in the 2nd harmonic alone, then half of what's remaining in the third, and so on down the line, giving a geometric decrease in THD for each harmonic. Then I look at crosstalk, I obviously want as little as possible. Then I make sure the amp is well shielded.
If all those check marks fit, you'd be surprised at how low in total power and gain you can get away with in an amp. The HD800 doesn't actually need much more than 100mW, if it's done right (and you don't listen at INSANE levels).