Spotify isn't profiting at all; that's the entire problem.
It's banking on the hope that offering a limited free tier will encourage some amount of users to become paid subscribers, while offsetting the cost of operating that at least a little bit by serving ads. It's unfortunate that you can't make sufficient revenue by just operating a free tier that's truly sufficient, but those numbers quite clearly do not work.
I mean, are you saying that you would be complaining less if Spotify simply killed the free tier? I rather doubt that.