Nothing should be dull or flat sounding on a 1.6k pair of headphones.
yeah, that is a good point but the sad reality is that component matching becomes much more difficult when the price goes up. i've had a pair of nad viso hp50's, those were brilliant because not only they had an enjoyable yet not bass bloated sound, but they were very easy to drive. same goes for meze 99's, you can drive them using an old ipod or any phone with a jack. the hd800s is hard to drive, it requires proper amping, and when it gets a matching amp, the reward is worth it. it's not for everyone though, it's a terribly time consuming hobby if you really dig deep.
You got any takes on headphone amps for wireless headphones? I might go and try on that fits in my pocket for travels/longer commuting
wireless headphones used in their wireless mode don't require additional amplification as the bluetooth receiver is digital, so you'll need to build in a dac and an amp inside them anyway. some wireless headphones offer wired connections, in that case they might (and probably will) sound better in wired mode if plugged in a decent source.
btw there are way too many portable amps that can sound great. older devices with built in batteries like the centrance dacportable (brilliant), chord mojo, oppo ha2 or ha2se, xduoo xd05plus (etc) already sounded nice with well matched cans but they were big to carry around. nowadays many manufacturers offer simple dongles that might take a toll on the battery life of your phone but small, powerful enough and sound very good. cheap and good ones include the apple dongle (volume might be too low though, i have one, it sounded not loud enough, i've read that it's due to some regional regulation that protects your hearing), and from that price point, you can pick one for every budget, the list is basically endless.