I enjoy listening to headphones, but probably only use them 15-20 percent of the time. Listening to headphones doesn't convey the sense of scale that a pair of speakers does, but they are great at night or in the morning when I don't want to bother anyone else. I have the HD800 (not the HD800S) and the Focal Elex, which is supposed to be kind of in between the Focal Elear and Clear.
I understand the HD800S is supposed to have made the HD800 a little less "clinical". I haven't heard them. The HD800 are great if you like to hear everything that's in the music. The Focal's are more fun to listen to and are still very detailed.
While some higher end integrateds, DACs and preamps have decent headphone amps, you're usually better off getting a dedicated headphone amp.
If you have situations where you'd like to listen to music and can't listen very loud because of others in the house or neighbors, then headphones are a great option (just don't listen too loud!) and you may find that you prefer the soundstage a good pair of headphones provides over speakers. You won't know unless you try.
I haven't heard the HD580's, but from what I've read they are similar to my HD6XX's which are inexpensive but far from mediocre. My suggestion would be to get a used headphone amp and see how you like the HD580's and if you find you enjoy those more, consider a higher end set of cans. Don't be afraid to buy used headphones, I have purchased many and just buy a new set of earpads for them.