Part of the answer to the OP's question is whether the high grade headphones are high impedance/planar magnetic or low sensitivity. If the headphone requires near 0.7W to power it well then obviously if you dispense with an amplifier or use a low power one the experience will be poor with lack of volume, distortion and other negatives. However there are plenty of dynamic headphones with high sensitivities that will be easier to drive. These of course won't sound their best without quality amplification but the degradation without a quality amplifier might not be that great. For me I just want the DAC and amplifier to get out of the way, I have a certain regard for them but I'm never going to spend lots for them. For high priced headphones I'm surprised more of them aren't supplied with a suitable flat amplifier as well as being burned-in as part of the package.
To your point, whenever this question comes up in relation to the Senn HD 600 or other higher impedance HPs, the answer here is pretty much always the same-- you need a better amp (or an amp period, if you don't already have one). Many of the lower-cost headamps I've been lookin at lately will have a switch, or in some cases mutiple settings for different headphone impedances though. If you already have something like that, or a higher impedance amp, then you may not need to upgrade to something better for a pair of high impedance headphones.
The flipside to that is that headphones with lower impedance which are easier to drive will generally require a lower impedance amp to deliver the best sound-quality, free of audible distortion. Someone correct me if I'm wrong, but I believe the minimum damping factor recommended for distortion-free sound for both higher and lower impedance headphones is somewhere on the order of 8-10 times the source or amplifying impedance. Lower ratios will probably give you some more volume, but also a bit more noticeable distortion.
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