There was an iOS app that used to let you do this; it would play music via Youtube embeds in a hidden web view, exposing its own UI for all the functionality you'd expect from a music streaming app.
Whether this was legal is... a gray area, it was a somewhat legitimate company that won some kind of Canadian startup contest on TV, but the music industry was, very predictably, furious at their business model.
Eventually, Apple got scared enough of being sued along with them that they caved in and removed the app, but that took far longer than I thought it would.
On Android you can use NewPipe for a similar experience. For obvious reasons it's not on Google's Play Store, but you can get it from F-Droid or Github.
Whether this was legal is... a gray area, it was a somewhat legitimate company that won some kind of Canadian startup contest on TV, but the music industry was, very predictably, furious at their business model.
Eventually, Apple got scared enough of being sued along with them that they caved in and removed the app, but that took far longer than I thought it would.
There's a good article at https://torrentfreak.com/apple-removes-parasitic-streaming-a...