Mixing with headphones is great IF the listener is going to use headphones too.
The reason studios use monitors it to get it to sound right no matter what the track is played back on. Most studios also have a crappy boom box to play the track on too, because even using a great set of monitors requires the end user to have great monitors too to get the same effect, so, they play it back on a cheap speaker system once they're close to a final mix and see if it sounds good still and make adjustments accordingly, usually needing to add more bass or separate the frequency ranges.
Yes. That is what I do too. Either in my personal studio or professional ones.