Summarizing experiences running HD6XX together with iFi Zen Dac from a power point of view. Note: I am using balanced headphone cables and also a power supply from iFi.
I would say that the Zen Dac manage to drive the HD6XX very well with my setup but it also depends on your setup and what you are doing.
A lot is depending on if you EQ your sound and by how much. If you EQ (boosting some frequencies) and lowering the pre amp value a lot you may getting closer (or hitting) to the limit, at least for soft music and classical music, also depending on the recordings/mix.
Also depending on source, running Tidal Hifi in exclusive mode giving me additional headroom (comparing to Spotify and not running exclusive mode). More complicated to EQ if running Tidal Hifi in exclusive mode though, it's still possible through Roon (and maybe JRiver, not sure).