This is a topic that is super-interesting to me. I absolutely hate that Spotify refers to "Your Library" instead of "My library" or just "Library".
My POV on this is that it is a case of ownership. The albums I save on Spotify are mine as long as I keep using Spotify. Another offender of this is Amazon. It's MY account, and they are MY orders. They also use "your" repetitively to the point that it makes no sense.
I think your suggestion that it is more clear to use both "your" and "my" in the same application is misguided. When's the last time a user thought that hard or learned a product that deeply?
My recommendation is for the product to cede ownership to the user. In cases like where that makes no sense, they should use no ownership label.