IMO the default music app being not very good is OK. The real sin is not allowing others to compete. Android default music player(play music, even the name is crap) is awful. But it's not a problem because there are literally hundreds of free and paid music players that will scratch your particular itch so well, that you won't be able to use anything else after that.
Have your tried something like Ecoute on iOS? It's a third party music player and I use it full time since Apple Music was trying show up everywhere in the music.app
Ecoute uses the same library as the default app, shows a nice simple grid or list of your albums/artists/playlists and is well designed. When you use any controls in either app it will be picked up in both. It doesn't matter in which app you start a playlist/play/pause/skip/whatever. With that in mind, using Ecoute as default app was as easy as replacing the icon in the dock. No need for a default music app setting in my opinion.
