HD800 and HD800S tend to prefer tube and tube hybrid amps. I used a Vali 2 until I had my Kenzie built.
That's a self-fulfilling fallacy, not a fact.
In my experience trying it, the HD800 pairs well with amps that are have globs of power headroom and ideally extremely low in distortion or harmonics. Its a very revealing headphone, where distortion in the system readily shows up. Be it the amp or the DAC source.
Coloration or not is a personal preference thing, not that it 'prefers' it. Its the users preferring it.
Try auditioning a Class A amp with loads of power, and a very transparent one. The Massdrop THX and the JDS Atom being well measuring candidates. And pair it with a good measuring DAC such as the Khadas Tone Board or the Topping D50 or the SMSL SU-8.
You'll be surprised how enjoyable it sounds despite people complaining about its "peakiness" and "glare". My experience was that its over emphasised by the distortion in lesser combinations.
As basis of comparison, I was listening to the HD800 hooked to a Chord Hugo2 that belonged to a friend.