I have got a pair of Stax electrostatic headphones and they sound like $50K monitors. Probbaly the best headphones in the world. BUT
Bats is sort of right too. It is not just about the sound. It is about other things.
Panning is a bit weird in headphones. When things are hard panned they sound very extreme hard panned in headphones compared to speakers.
Also reverbs are a bit weird too. On phones you will hear reverbs very well even with only small amounts of reverb. However on speakers the reverb will be non existent and very dry. You have to alter it.
There is no substitute for speakers in the end. I may do a lot of editing and even some premixing on cans but really at the end of the day it is the speakers that only really tell the true story.
But even after doing a great speaker mix I think if the end product is going to be primarily heard on ear buds for example it is wise to run your mix into some and have a listen. I have done this and had to alter the bottom end slightly to make it work on the earbuds. But I did do the mix on speakers first.
Tell you where headphones are fantastic though and that is precision editing and editing out micro sounds like blips and blops and musicians knocking stands and very small things you may never hear on speakers. It is like a magnifying glass into your tracks.