Just a ride sharing app cannot reach the scale and revenue to justify the investments they have attracted. It is not realistic to raise $25+ Billion[1] just to be a pure SaaS startup.
Both Uber and Lyft[2] run rental businesses already, the model works where you can rent a car on a weekly basis just to drive on their apps, they cover maintenance and other services.
Uber will have to find a way to maintain their growth, and Lyft probably will be acquired by a rental network. The result is the same vertical integration.
[1] Uber's equity investment so far. SaaS startups can be valued lot more even $100s of billions, but pure tech companies do not raise that kind of cash. Stripe for example despite its delayed IPOs and ESOP issues has only raised $8B.
[2] They own some of the inventory and rest are from partners I believe.