Older software sometimes runs just as fast on older hardware, too. It’s anecdotal, but I never remember waiting on Winamp to start up. iTunes, on the other hand, has always seemed slow.
Me neither, but I remember I was annoyed few times it took "ages" to load a "library" of few (thousands) tracks and then consumed considerable amount of RAM. Maybe TENS of megabytes even (!!1!).
So I remember the relief when I switched to Billy audio player [1], that was way more "spartan" and had just those few features I really needed, and then joy of even faster start time and negligible memory footprint.
[1] https://www.sheepfriends.com/index-page=billy.html (download is "temporarily off", but there are comparisons with Winamp and screensot).
I'm not overly familiar with that period's iTunes, but I remember when I bought my first iPod, a 4th gen click wheel (don't remember the year, but it was already an "older model" at the time) I was using Amarok on Linux on an AMD Thunderbird with 256 MB of RAM. That thing would fly. And it did more than Winamp: it had an actual DB-backed music library, iPod interface, etc.
Yet, a few years later, when I got a MacBook Pro with a dual-core CPU and 16 times the RAM, iTunes would still be painfully slow. And I don't remember it doing much more than Amarok. As a matter of fact, it was inferior on pretty much every metric I could think of.
This was years before YouTube was even founded
This is a hilarious statement to read, cause that's probably what 80% of people were using iTunes exclusively for and relegating their music listening to their iPod/iPhone, especially in the later part of the 00s.