They can start adding support one city at a time. And for the Uber user, the Waymo option only pops up for you if the ride you requested is within the Waymo range and they have cars available.
This way they can also collect tons of data about how users respond to the offers, affinity to driverless cars per region, price elasticity, etc. And then dial the supply up or down as they wish. They can even start covering a city with just two cars if they wanted to, and then build popularity and word of mouth.
On the other hand if they started with their own app, the lack of car coverage in most areas (due to low car supply, pending regulations, etc) would quickly frustrate users who would then switch to another app, so user retention would be a nightmare.
Not to mention side-stepping all the customer-facing operations of running such a business, which Alphabet does not have an affinity for.