The new payment system unified all of these into pure money movement where any entity can move money to any other entity. This enables all current and future products to have flexibility in payment models. (Think about how payments would be modeled for Uber Freight or with the new Uber Transit partnership [1])
Source: I work on the Uber Payment System
[1] http://www.businessinsider.com/how-uber-masabi-mobile-train-...
What we have built at Uber is a realtime system that is reliable, provably correct with high availability.
As I've said in another comment, for many other systems, if it fails, people can just try again later. If we fail, someone's mother, grandfather, son or daughter are stuck on the side of the road in the middle of the night somewhere. Our needs (or at least the standard that we put on ourselves) is higher than many other payment systems.
I'm relaly impressed with the diversity of their offering as well:
https://www.adyen.com/pricing/full-list
I'm currently in Japan and it's actually relatively common to pay for things at the convenience store here, I'm amazed they support it.
"I joined Uber two years ago as a mobile software engineer with some backend experience. I ended up building the payments functionality in the app - and rewriting the app on the way".
Following the "rewriting the app" link in that paragraph takes you to another page "Engineering the Architecture Behind Uber’s New Rider App" - although that's co-written by two people, neither of which are the author of this article it would seem.