I don't think Uber is going to completely turf out, but I believe they will experience a correction in their valuation.
It looks like they last raised money at a $62.5 billion valuation [1], which suggests that investors are expecting the company to operate at a global level. Unfortunately, Uber is facing extremely stiff competition in China [2] and India [3]. There's also the well-publicized tension between Uber and various European companies. And that's not even taking into account increased regulation in US cities like San Francisco [4].
So, while Uber is clearly a successful company - how successful will it be? $62.5 billion dollars successful? My guess would be no, which would drive a correction for the company.