Music is via Spotify, or, rarely, via the music app which has content in the cloud. Spotify stores my music locally. The App Store doesn't have iTunes in its name on iOS devices (as far as I can see). If I wanted music on my device via the music app, I'd buy it from the store. However if I owned a CD (not sure how this would happen, binned them all ages ago) I would have to stick it in a Mac (not mine, it hasn't got a drive), rip it, put them on a memory stick, get it to my Mac, dump them in iTunes (argh), then wait for cloud sync.
It helps to not conflate iTunes (an application) with the iTunes Store (a service). The latter can be accessed either from the former or from a handful of roughly equivalent apps on the device itself (an App Store app, an iTunes Store app for media, a Podcasts app...) There are very few things one cannot do without the former — which is good, because odds are that, when someone is talking about how bad iTunes is, they're criticizing the desktop application specifically.
Also, as an example use case, how else do you put music on your iDevices? I'm under the impression that you have to use iTunes.