This is entirely tangential and probably a pointless gripe in this thread, but...
For some reason, it's always really annoyed me that Apple took MP3 players, called them an 'iPod' and suddenly everyone ate them up like they were the second coming of christ and we'd never had them ever before.
To be clear, there were good non-Apple MP3 players, but they were either marketed poorly, or late arrivals (e.g. the Toshiba player that got rebadged into the Zune). By the time those existed (and tech companies started hiring UI/UX people), Apple was doing a complete reset of another product category: smartphones.
I suspect history would have been different had, say, MiniDisc hadn't failed horribly in America[0]. Pre-iPod, portable music in the US was either compact cassettes with all the downsides of tape, or CD players that could just barely fit in your pocket. The iPod was such a step up from either that it all but became a genericized trademark. Had we had a competing technology from not the 1980s, we probably wouldn't have thought the iPod was so great. Or at least, people I knew who had MiniDisc looked at the iPod like I look at all the e-waste that was trying to compete with the iPod.
[0] Yes, I know that Sony was basically trying to avoid a repeat of DAT getting banned
The iPod is the only Apple product I have ever purchased. I could easily operate the iPod without having to looking at it constantly which was great for bike rides or car rides. No fiddling and taking eyes off road.
The iPod cam with a large screen and a click wheel. I could find songs on it. That was a revolution for me.
MP3 was the enabling technology (if you can't fit many songs on a small device, then this is moot).
As others have eluded to, MP3 only didn't seem to be enough. I remember passing on early mp3 players because they only had 32-64mb of storage, not even really enough to store a single album. Snatching up those tiny 1.8" hard drives right away and integrating them is probably as important as the UI improvements because it solved that problem.
As soon as I had the funds I quickly moved onto a variety of CD/HDD based players, although I've only recently bought (and modded) an iPod - there's definitely reasons they were so popular. I can appreciate why they went to the common platform with the phone and were later phased out entirely, but as a task-dedicated non-smart device they would be last-man-standing.
That 1G of flash storage at the time was huge for a phone. This was before everybody had an iPod Touch or iPhone, of course. iPhones came out the next year but in my area hardly anyone had AT&T, so because of the exclusivity the iPod Touch became popular way before the iPhone in my area.
Flash based players were smaller but limited in size and expansion media was expensive. Hard drive players were hobbled with USB 1.1 connections and an obsession with drag and drop for management.
The iPod by default just synched with your iTunes library. The FireWire (and eventually USB 2.0) did so quickly. The navigation was as good as the metadata which iTunes made easy to edit. The UX on the device made scrolling through long lists of songs very easy.
The iPod made using an MP3 easy and approachable for normal people. The Rio, Nomad, and a multitude of others did not. They included a bunch of checklist features but didn't focus on usability until Apple dominated the market.