I would argue that most of these Postgres "flaws" are actually advantages over MySQL when you look at them holistically rather than the very specific Uber use-case. Postgres's MVCC is superior (can rollback DDL, can add indexes online, can have open read transactions for a VERY long time without impacting other parts of the system) Postgres supports many types of indexes, not just b-tree. One thing it doesn't have is…
They have a couple posts about "Schemaless", but I still don't understand why they used MySQL as the data store instead of something like Cassandra. ( https://eng.uber.com/schemaless-part-one/ ) From that post it looks like they basically built a no-sql database on top of a relational database.
The only reason given was operational trust ( "If we get paged at 3 am when the datastore is not answering queries and takes down the business, would we have the operational knowledge to quickly fix it?" ). The project took nearly a year to roll out, and in that time the operation knowledge could surely be trained, hired, or contracted.