Here’s a few guesses:

1. It’s not 100x (or even 2x) faster or significantly more stable than Apple Music

2. It’s always easier to make a nice app when starting from scratch versus trying to fix existing older software to be nice

3. Apple did a good job with their APIs

Yeah I don't think it is any faster or more stable than the actual Apple web client. They probably use the same API's. Plus lots of considerations that applies to any website. Is it available in multiple languages? How accessible is it? Does it work on older browsers? Also, digging around, the Apple web client seems pretty up to date. Isn't old software. I like the search feature though on this.