They want everyone to use the official app so they can advertise to paid users in the future. It's the cable TV model: get people to start paying for subscriptions by offering to remove ads, then slowly trickle the ads back in.
A paid tier lets you easily identify which of your users have disposable income, and then you can sell the ability to advertise to them at a huge premium.
Spotify's advertisements are quite different because they're basically worthless. Nobody wants to pay money to advertise to broke people. Their free tier exists merely as a funnel; the advertisements function as intentional annoyances to nudge people into paying for a subscription.