A corollary of this is that whilst meta-search engines didn't take very much of the pie for themselves, the fiercer price-competition they imposed did take a much bigger chunk out of airlines' margins, and particularly the margins of travel agents reselling airline tickets.

Uber at present is a travel agent, not an airline

Just as they have, interestingly, in the airline industry. Most people go to kayak, hipmunk, skyscanner, monondo, etc. The existence of meta search engines are a hint that the service is a commodity and margins will be slim.