Uber has to do a lot of checking to ensure that their drivers are safe and reliable. The family of the first person that’s killed because of a intoxicated, ex-felon Uber driver will sue the pants off the company. It takes time and effort (= money) to get everything right. Uber’s margins are probably pretty good, but they need the 20% to cover all of their costs and overhead. Plus the costs to support their app etc.
Uber.com provides absolutely everything except the seat for the passenger’s butt. Without the supporting framework, publicity, app, servers, and web of interconnection, the driver would be essentially useless. Few people could go around scaring up enough rides to be profitable as an independent.
I assume they have to maintain some kind of insurance, they have a business, they probably have rent/mortgage (in a building with electricity and plumbing etc), they run commercials on TV, the owner takes a profit and all kinds of other expenses and they’re doing it all for 20%…that’s not too bad.
Also, keep in mind that unless they ding the drivers (like groupon), credit card transactions usually cost about 3%ish, so there’s that.