That analogy doesn't hold. When I search I need to search the whole internet. Google will generally be able to deliver the best search results for all searches in all places all the time. That will never be true for transportation, taxi and car services will always have an aspect that is permanently fragmented.
As long as it's possible for a small group to compete with uber even on the margins, Uber will never have monopoly pricing power. Someone can always start a small company to take people to the airport, pick up executives, etc. Anecdotally, most serious travelers I know in NYC have reverted back to using car services to do airport trips, since it's a much more predictable experience than Uber.
As long as that's the case Uber will never reap the windfall profits that accrue to a monopoly. Which makes me seriously wonder why they would burn such remarkable amounts of money thinking they can establish one.