The "don't look at the man behind the curtain" answer is that Uber will magically become profitable at some future date, soon, when robot taxis are invented for use on the road, Uber procures thousands of them and they take over.
Some will go under but some new will appear. In long-term uber like companies can't win and make monopolies as tax business is not that hard to get into
Indeed. In quite a few places (Australia, for instance) the taxi industry is basically a government protected cartel. State governments charge insane amounts for taxi licencing (to get their cut of the cartel rent) and then restrict supply of taxi plates (to maximise their cut). Consequently, it was recently not uncommon (in Australia) for resold taxi plates to go for mid six figure sums on the open market. It was nuts.
I think Uber has changed this, although they're basically using predatory pricing as their market strategy. I must admit I have mixed feelings about all of this... Who knows? With two anti-competitive colliding like this, maybe we'll somehow end up with a competitive market at long last...
https://en.wikipedia.org/wiki/Predatory_pricing
Silly me wonders if Uber will run out of cash before (enough) taxis companies go under.