Just to add a bit of my own opinion, I find that it only takes about 15 minutes of listening to headphones, before my ears get completely fatigued. It is like I am not even in the same room as the music. There is an unnatural feeling that is surely based upon the human brain not being accustomed to isolation from things going on around us. That being said, I love to listen to a final mix, or any well mixed recording on headphones, but when I get up and move around afterward, I feel a bit off balance. That in itself says something to me.
Mixing in the real world, as vague as that should sound, should be in an environment that is comfortable. Importance added to that, would be accuracy. The levels of accuracy are dependent upon how well you can get your mixes to translate on others listening systems. You could mix on the crappiest set of monitors, and get good at it. You would likely get there quicker with a pair of monitors that were more telling of what you are hearing. To expect great results from even a decent pair of headphones, makes me cringe in the fact that I know what they do to my head. Some say they can do it with them. Most people that 'are' capable of this, have spent more $ on headphones, than I have on monitors.
To answer the original question, I would say, 'In my strongly versed opinion, based on my personal experience, there is no friggen way I would ever even attempt to think that it was possible to ever even come close to getting a reliably translatable version of a decent mix, that I would even show my Grandmother, even if it was her last wish, with using a headphone mix alone.". There is just more going on between 'left' and 'right', that headphones do not allow to be heard, due to the isolation.
If your mixes are only to be heard by others using headphones, then sure, mix for that. I doubt it. Most people live in an ambient room society. Use tools that work there. And, get out of your own head-headphone guyz....
Just my 2.5 cents. Probably worth .2.