The $450 I paid for my endgame headphone/amp/DAC wouldn't even get you in the door of an audiophile speaker place.
I think the main reasons were being able to experience the sub frequencies with my entire body (they're too big to fit in your ears!), and share the experience with my friends.
It's hard and expensive to move a lot of air precisely, and speakers are influenced by room acoustics. $5 headphones beat $50 speakers. $80 headphones beat $200 speakers. And $200 headphones beat $400 speakers.
I can't afford to find out beyond that, but I suspect things get more nuanced on the ultra-high-end.
For me, for music, I'm happy with something like a Sony MDRV6 studio monitor, which sells for under $100. I don't know of speakers I like under $200.
Headphones are also nice for teleconferencing, where speakers aren't.
I say this as someone with both Sony MDRV6 headphones and a home borderline audiophile stereo setup retailing for over $3k.
TBF I was powering the headphones with just my Pixel 3, but it's not a particularly hard to drive headphone.
There's been quite a bit of advancement recently with bluetooth speakers, and we'll probably see some more disruption in the affordable hi-fi space soon with what Purifi is doing with Class D amps.
The headphones will give a more faithful reproduction of the original recording.
Making a nearly-perfect class D amp isn't hard (which is not to say a lot of people haven't messed it up; there are a lot of pretty bad amps out there).
The hard part is the speaker itself. The mechanicals of moving a lot of air accurately are hard. You need a physically large woofer which moves over a long distance. If you do that, your woofer and tweater won't be in the same place, so your phase response will be wonky. You don't want the air cavity acting as a spring overpowering your driver, so you need a large box. Etc. By the end of it, it's super-complex. Headphones are super-easy in comparison.
Secondly, you arguably get more bang for your buck. For a budget of say $300-400 split between open headphones and a DAC you'll get much better sound quality than similar money spent on speakers and an amp. Finally to get the most out of speakers you need space to set them up correctly and a room with decent acoustics. Headphones avoid all of that.
But you can certainly wear them in your cubicle or home office without any issues for other people around you.
Especially if you work from home and have an office that is a room on its own (i.e. garage or basement) open-back are a no brainer for me.
And also open backs just bleed noise, they don't shake the room, so unless someone is next to you they aren't gonna hear anything anyways.
I put together a ~$3k system recently that has blown away any headphone experience I've had [0] [1] [2].
I guess for me, the experience goes beyond just what the music sounds like. Being able to dance without having to worry about anything falling off of my head or out of my ears, and being able to share the experience with my girlfriend and others effectively multiplies the joy I get by an order of magnitude.
[0] https://www.minidsp.com/products/streaming-hd-series/shd
[1] https://vtvamplifier.com/product/vtv-amplifier-stereo-purifi...
[2] https://www.parts-express.com/solstice-mltl-reference-tower-...
Edit: For their dollar that is. With unlimited money I would probably take speakers.
Reasons that I can think that someone might still go with open backs are:
• Portability - You can move around your house or go running without leaving the music.
• Less dependent of environment - they basically sound the same in a small, big, or acoustically reflective rooms.
• Leak less sound than speakers - you can blast music without waking up your kids or downstairs neighbors.
• Better high frequency reproduction - whereas full sound systems will generally do better with lower.
EDIT: Added price stipulation to where speakers start to sound better. Agreed that if you're not willing to spend much and want to listen alone, headphones are the better choice.
With headphones, I can still hear my music at a loud volume with high quality while the noise outside of my home office is none. The only time someone would be affected would be if they walked into my home office.
If I set my speakers to the same volume level, it'll disturb most nearby rooms in the house.