Mixing on headphones is a unique use of your hearing system (your ears and more importantly the way the brain has evolved a fantastic processing of what comes into your ears). It has NOTHING to do with listening to things in the real world where sound bounces off things and comes from all around you in a complicated collection of short and long bounces off of everything around you. Your brain can decipher these and come up with a coherent reference of your surroundings and the end result is a 'nice' sense of listening.
We listen to artificially created music and sound primarily on speakers. THat's what the end user will be doing and that's the benchmark. Pop on a set of headphones and you're in a COMPLETELy different perceptural world and while you DO hear things you wouldn;t notice in a room with speakers, you also do NOT hear other things you want to know about. spatial positioning is COMPLETELY different as are relative levels and the tonality of any sound. There's nothing wrong with listening for moments at a time on cans to check something particular but mix on them and you'll make big mistakes unknowingly. Biggest one is folks trying to use 'phones to 'isolate' themselves and make critical decisions on mic placement or eq choices when tracking in the same room with the instrument. You'll screw up the bass ballance at the least... usually worse.
Headphones force you to listen to the isolated picture that the recording itself offers. While that can be really enjoyable in itself, and even a specialised unique way of listening (you CAN 'mix for headphones' if you KNOW that NOBODY in your intended audioence will EVER listen on speakers, and do a few tricky things you can't on speakers), still, from your bedroom to the 25,000 seat arena, speakers in a room give your brain more clues about the sound than headphones do. Mixes that work on speakers translate dandily to 'phones... you will NOT make a choice on a speaker mix that sounds godawful on cans.
it does NOT work the other way; it's satanically EASY, so easy it feels GREAT, to make 'really cool sounding choices' in headphones that just reek on speakers where you'll be horrified to hear key elements of the mix vanish, sound odd, sound BAD.. ANYTHING can happen, even using teh BEST cans. The best sounding headphones I know are the STAX Lambda Pros (and lately the more reasonaly priced Beyer DT990's and the most brutally accurate the 48's) ... I've done many many location classical (and other genre) recordings with them and just have all sorts of personal little intimate physical reactions to listening to ANYTHING on them. But and I'd never use them to guarantee a final record mix to go to distribution. I'd go to as many different sets of speakers I could find and compare. At those same location recordings i would RATHER have (and often DO have) a decent set of high fidelity speakers in a room far from the performance to KNOW what I was getting.
But you want Isolation? The following concerns ANY judgement made on the sound of a mic placement and MOST especially any judgement made on a MIX...Repeat after me... If you are where you can hear the thing you;re trying to record AT ALL with headphones off, by just popping on a set of headphones You Cannot Hear The Tonality Of The Instrument To Make Important Mic Placement Judgements Fairly. We do it all the time when we HAVE to but we HATE it.. unless we can walk throught the door to the room with the speakers, shut the door and listen for real to know what was just done.
Imagine trying to drive a car with only a tv camera pointed straight ahead and you have to watch the monitor. It's a lovely picture with nice colors and maybe you can even zoom the camera in to see if that brown lump up ahead is a flat burlap bag or a newly dead groundhog, but you CAN'T tell what your driving environment is like. Can't.