It's good to avoid the marketing trap. I believe that once you have a quality DAC and or amp, easy enough to find, the story about scaling is more about marketing than appreciable sound benefits. IMO belief is a scary tool for marketing and forums. I believe that headphones are where you'll set the stage for your listening experience.
I don't know if you'd need a quality DAC, there doesn't seem to be much sound quality difference between the different DACs that I've tried, mostly in sound signature. A good amp can be useful, if you have hard to drive headphones. Or if your DAP has a really weak amp section. But there seems, to me, little point in getting a DAC/amp that costs more than your headphones (which seems to happen a lot on Head-Fi). As you say, the headphones have the biggest impact on sound (quality and signature).
I have a really different approach from you, I like almost all headphones that I listen to for their different sound signatures and have kept most of what I've bought, and with DACs and amps I've pretty much kept them all also. I do have 3 different area in my place where I listen so my gear is spread out over these 3 areas and my GF also uses it so its not like its just sitting there. And when my son visits during breaks from college and my GF's daughter is visiting having extra gear around is nice so everyone is happy. Another reason is I like the idea of "using the right tool for the job" when listening to various genres of music, classical on most closed headphones is not very good while EDM or bass heavy stuff will not sound great on very open bass lite gear.
I can appreciate that. I had a HE-560 for a while as well, which had a bit more oomph in the bass than the HD800, but was in terms of sound quality really similar. And the extra bass can be nice for electronic music that I listen to. And the HD800 can be a bit tiring with some death metal (though that is in no small measure because of the mastering as well). But in the end I don't want two expensive headphones, and I don't really swap between headphones that much either (switching every other song would be a hassle, as I always listen to large playlists on shuffle). And the HE-560 was always noticeably different in sound signature than my speakers, which I listen the most to, and which I enjoy listening to the most, which is not always bad, but it reminds me of the way the HE-560s were not quite what I would call neutral.
Therefore, I just stick to one headphone. It works best for me, though I understand your point of view as well.
oh boy I wish it was this obvious for everybody. more so for newcomers seeking advice so that they wouldn't take everything at face value. (I have a dream!)
Ok, you shouldn't take everything at face value, but most posters are not exactly very moderating in their experiences either, and occasionally if you see a big thread with only praise, and you don't have the option to audition something yourself, you might start to believe that this particular headphone / amp / DAC is what you might need for a better experience.
And when you get it, and depending on your nature / mood, you either convince yourself that the posters were right, or you realise that despite the flood of posters telling each other one thing, they don't necessarily match with your experiences.
I get the impression this is because if you're buying or using an HD 600 these days, you've already to some extent eschewed the pursuit of the latest shinies, or at least you can see them in the context of being incremental improvements at best, and not life-defining objects.
Not only is it not the latest shiny, it is also not considered TotL. De HD800 is also not the latest shiny, but moderation can sometimes be hard to find in that particular thread.