My impression as a high-schooler (at the time) of what made the iPhone so captivating for others, was that it had Shazam, and all of the features of the iPod touch, and all of the features of iPods before the touch. You could hold your phone up anywhere and learn what song was playing, and as far as I could tell that was basically it; very much a fashion thing like Starbucks (before the unjustified popularity of that also died as they stagnated). I thought people were a bit silly for spending so much on a phone then, and still do, because by the time I eventually got a "smartphone" with a touchscreen, there was enough competition in the market that still to this day I've never felt compelled by any phone product >$600
I had the iPod Touch and iPhone relatively early (well, much earlier than the general population). I don't remember Shazam being important at all, I think I only discovered it a few years later.
What blew pretty much everyone away that I showed it is how incredibly smooth web browsing was (remember, there were no apps on the original iPhone and even after that it took a little while for apps to really take off). Most smartphones at the time had clunky resistive touch screens or even little joysticks to move a mouse pointer. With the iPhone, you could scroll with your fingers and it was butter-smooth (at least for the day). The iPhone was a game-changer because you had a device in your pocket that you could browse the web with and it was at least as easy as on a desktop, if not easier.
Just for comparison, this is how you browsed the web at the time on probably the most iconic smartphone at the time (Blackberry):
I think that's a fair point, but I definitely wasn't speaking from the perspective of even the first iPhone version, more from point where the general population had access to them, and my impression was that they enjoyed the novelties that seemed heavily marketed at the time, Shazam being a very relatable problem for almost everyone.
Not only were there Shazam apps on phones pre the first iPhone, but in the first place Shazam was a service you didn't even need a smartphone for! When I first started using it, they had a telephone number (in the UK, I'm not sure which other countries) to call up while music is playing, and 30 seconds or so later it would text you the song that it detected during the call.
I agree that "combining phone with one of the most popular / best in some ways mp3 player on the market" was a big part of it (with web browsing and video playing equally important), but Shazam wasn't a new thing that iPhones brought us.
(I also agree with danieldk that Shazam just wasn't a significant factor for most people on any devices, before or after iPhones.)
That's an interesting bit of history I didn't know about, but my point wasn't that Shazam was a new thing exclusively for the iPhone, but it was among the novelties that helped market it along with the other attributes we agree on. I think the most compelling reason was fashion, not so much technical, because really I didn't know anyone with the very first versions anyway.