Main-amplifier integral h/p amps are generally a kind of free 'add-on' and okay but nothing special. If one engages in a lot of h/p listening, a dedicated amplifier is essential.
With a lot of headphone use in evidence, I'm surprised that Naim haven't revamped the long in the tooth and average sounding (to these ears at least) Headline; or indeed developed a much more 'serious' and higher-cost device. The Headline is a daft bit of kit; ideally requiring a Supercap to give of its best - then becoming overpriced for its performance level.
There are many better, (and simpler one-box) h/p amps out there; and as ever, one must simply listen and find a good synergistic match with one's chosen headphones.
Come on Naim. Make a really good headphone amp. The market is crying out for it.
I agree that I was hoping Naim to come up with a Superline level 'phone amp (with cct. board on a floating brass slab etc..), I disagree regarding your assessment of their current Headline 2 particularly with HD800.
I was in a search of better closed can a few years ago so I went to a Head-fi meet with my HL2 and NAPSC to hear various headphones.
Boy, did I hear a lot of *crap* headphone amps!
HD800 was everywhere and driven by many different amps both valves and solid state and guess what! the HD800 sounded the best with my humble HL2/NAPSC.
Now this was before Sennheiser came out with their own amp for the HD800 so I do not know how it fairs, HL2/HD800 ( with a proper source ) was most enjoyable for me.
As far as the use of a SC with HL2, it certainly isn't a mandatory I feel as even a littlest NAPSC has the Naim sound I love in spade. I certainly did not get this when I was listening via non Naim amps.
Provision for a chassis mounted DIN socket would be also nice as I think that the stock captive plug is limiting its performance. ( albeit it is generally much better than various non Naim aftermarket cords I have tried so I could see from the factory stand point, having this is better than using a less than optimal none Naim cable )
I got mine modified and used a Hi-line, there was a marked performance boost. I've no doubt that Super Lumina also can be good here.