More notably, dedicated MP3 players like the Ipod Classic, or various ones by Sandisk, etc.? Is it because you also want a device that can access iOS?
Maybe it has to do with whether you were in the habit of carrying your music around before the iPhone came along? I wasn't. When walking around cities and suburbs, I prefer to be in contact with my environment, rather than block it out. Fundamental safety. In the forest, I'd rather hear birds than Resphghi's The Birds; Schubert's Trout and Beethoven's 6th are more evocative when I'm
not surrounded by nature.
If you're the sort who prefers to leave the phone behind; if music is your refuge and escape, then clearly, a separate music player makes sense.
I have a hard time understanding why anyone would carry two items in their pocket when they can carry just one, unless they generally carry either one or the other, rather than both.
If you're the sort who wants to have your information, communication, and computation available at all times (and that information and communication device also includes a dandy music player), there seems little or no point to carrying a separate music player.
I love the integration. If I am listening to music and my phone rings, or Siri is providing turn-by-turn driving instructions, the music pauses and resumes automatically. The same headset can be used for listening to music and answering a call. Since I have a nearly constant data connection, if I have an uncontrollable urge to hear a piece of music that hasn't been pre-loaded... I've got it.
I'm not sure what "access to iOS" means to the OP. iOS is an operating system; a user interface. Tabula rasa. It's a means to an end: Access to telephone, camera, text messages, email, web sites, news, stock prices and sports scores, banking, reading matter, journal, calendar, games, photo album, pocket calculator, guitar tuner and songbooks, business documents, audio recorder, dictation device.... This is an
incomplete list of the features I
routinely use. And in most cases, the built-in music player will continue along on its own, without interruption. When it is interrupted, the interruption makes logical sense. So yeah, if that's "access to iOS," why would someone not want it?