Uber is pretty formidable in building and growing a two-sided market. I suspect it's tuned continuously, at high resolution (in space and time), with levers I mostly don't know. And that's got to be a big contribution to the complexity of the stack.
This of it this way. A standard e-commerce site, or SaaS with low-touch marketing... there are a crazy number of KPIs to monitor, loads of levers (e.g. what's the right discount to fix basket abandonment). The instrumentation to track all these conversation funnels (and to do A/B tests to see what works) is half the job.
But at least we have a common understanding of the metrics and the levers -- for SaaS, say, there are tons of similar services, and the knowledge is shared in the community.
Uber? How do you grow while maintaining market liquidity every evening of every week? If you artificially hike demand from passengers in a particular neighbourhood (say with coupons), does WOM amongst potential drivers work to increase the driver pool before the passengers get frustrated and move to Lyft?
All of this is new. So how do you create the tech to track not just all the data you need, but all the data you might need, plus the capabilities to do tests to figure out what levers to pull? Hard.
I have no particular insight into this. But my guess is that Uber isn't flying blind - their growth has been no accident - and the complexity of their tech is due to instrumentation not operations.