The premise is little flawed since people still like to own cars. Therefore future self-driving Teslas will be in the hands of people on a scale much larger than the future uber self-driving fleet.
This leads to higher levels of data collection and more accurate, up to date, maps. Uber is always going be behind with this with no solution except in small city centers which it should be fine.
I would almost argue that Otto, bought by Uber, hasn't really demonstrated modern self driving like Tesla or Google. So I think they might be a ways of still.