Creating a music streaming service from the ground up is no small task. As great as some of Tesla's products may be, there is no way a proprietary music streaming service will compete feature for feature with other services that have been doing this for years. Look at how long it's taken for Apple Music to really catch up to Spotify. Some would argue that it's still not quite there. At launch, there will be hiccups and bugs and surely will be missing some features that customers expect.
There's also the problem of adding another streaming service to the mix. In addition to Spotify, Apple Music, and Google Play Music, there's Pandora, Amazon Prime Music, Tidal, and more. Customers tend to join one and stick with it. Some have been with their particular service for years, and nothing short of a complete shutdown would force them to migrate elsewhere.
While Tesla may be in talks with some record labels, it's going to take a lot to secure the rights to the same range of music as other services. It's taken years for Spotify and Apple Music to fill out their libraries. Some labels and musicians were holding out for more money or simply didn't like the idea of streaming versus buying. Don't expect an artist-for-artist lineup for Tesla's service.
Tesla is currently hard at work going up against established automakers. Adding in another monumental fight would be stretching money and resources thin. While Tesla has done a great job of joining the fray and forcing an industry to change, competing against tech companies requires a different set of skills. These companies are open to change and quick to pivot to meet new competitors. Despite a great market valuation, Tesla has never turned a profit. Investing a lot of capital into a new music streaming venture at the same time it's planning car production in China, developing new models and expanding on other fronts seems wasteful and a distraction.
There are plenty of complaints right now about Tesla's lack of Android Auto and Apple CarPlay. Tesla's infotainment system is one of the weakest parts of its vehicles. While it's not alone in having a lackluster infotainment system, the addition of Android Auto or Apple CarPlay would go a long way toward helping it. Customers have been vocal about asking for it.
There is one big benefit for Tesla. Not being tied to another company gives Tesla some amount of freedom. With an in-house service, Tesla controls everything. The thing is, Tesla already has Spotify integration in Europe. It's already given over control elsewhere in the world. Customers there seem happy with the service, so it's hard to see how the benefits outweigh the cons.