If the cops hadnt also aggressively pursued people "stealing" music (a bullshit proposition to begin with) Spotify would not have won. For most people avoiding a potentially big fine, even if the chance is small, tips the balance into just paying a few bucks (which is itself a huge price concession from the music industry, who would love to charge what CDs used to cost) - but they cant, that would tip the balance back into piracy
True that the full win was due to copyright enforcement by various actors.
However, in the early days of Spotify the ”play any song with a click” was pure magic and nothing piracy could compete with.
A fun anecdote from that time is also that basically the whole Spotify catalogue was full of pirated music — they had not yet secured any music rights and I personally thought they never would succeed with that.