I was thinking about this a lot last weekend...First, we're talking about a number of things here, at minimum
1. frequency response of headphones on our ears (and also "correcting" that response with EQ—especially to a "speaker in room" curve)
2. binaural room simulation—this is what really aims to "sound like speakers"
3. angled drivers—delivering sound coming from in front of us, as we normally listen to anything
I don't have angled drivers, I won't discuss—I guess for most people this isn't the most important thing, otherwise all headphones would be made that way by now.
For people who primarily listen with headphones, I'll guess that #1 is the main topic of interest. But also, I think such people don't spend a lot of time thinking, "if only these sounded like speakers". Most accept and even like the sound of headphones.
For me, headphones are mainly for tracking (most routinely, recording vocals, since I otherwise play electronic and electric instruments), and what I scrutinize tracks with (a/c noise? lip smack? kicked the mic stand?). When I picked up new headphones recently, I started paying more attention to how they behaved with music.
So, with a goal of listening to audio as it was intended to be heard, #2, to me, is clearly the most important. I always accepted headphones are what they are, but with these new thoughts in mind, it was surprising to me just how wrong many recordings are on headphones. On denser mixes, some of the tonality and balance is clearly "incorrect" compared with the intended sound, but not necessarily bad. But on some sparser mixes engineered for a wide image, the results can be pretty awful even on classic recordings. Say, some older Black Sabbath, before the age of quadruple tracking and harmonies on everything, with stereo spread.
Oh, and there's also Apple's Dolby Atmos binarual music—another topic.
Anyway, I'm still playing. I already have had Waves NX for a long time, and had only played with it for amusement, but I picked up CLA NX (sim of Chris Lord-Alge's studio), an improvement, and picked up SoundSource for the Mac to make it and headphone EQ easier to deal with globally. I still probably won't spend a lot of time listening to headphones for pleasure (don't sit still for long enough anyway), so the question is will I do some headphone mixing...right now I'd say I will not attempt mixing without a room sim like NX, it does change everything in that regard.