A few points on that.
1) Totally agree that Uber will not be the manufacturer of the first wave of true AVs. That's likely to be whichever manufacturer Waymo is partnered with in a few years.
2) The value you assign to AV-enabled Uber is going to be related to whatever value you assign their brand name, gathered data, platform maturity, mindshare, marketing ability, and cash pile. It's technically not all that difficult to spin up a competing dispatch service to Uber, but it is difficult enough and capital intensive enough that there are very few competitors in most markets. Notably absent are the potential AV manufacturers who would basically be starting from scratch unless they grabbed Lyft at a discount or something.
3) It's important to define what "soon" means and what scope you're talking about when making predictions about AVs. Waymo is legitimately looking like they will be ready to launch true driverless vehicles for taxi service in select markets and conditions in under 5 years.
Given the above, the question is can Uber last long enough burning cash every quarter and still remain a market force by the time it's in a position to leverage AVs? I don't think so, but I'm also not shorting the stock.