The vast, vast amounts of money they spent on driver incentives city by city would seem to support the OPs claim (source: I was familiar with their spend on ads in the US approximately 10 years ago).

Do you have a source for the claim that Uber was making money on rides during its decade of enormous unprofitability?

Its public stance was that growth was more important than profit. Why wouldn't they be subsidizing rides to fuel growth if that is their publicly stated goal?

And anyway, we got the Uber Files some years ago which made it explicit:

"In October 2014 in Madrid, the presentation shows, the hourly subsidy to drivers of $17.50 was almost twice the hourly fare it charged, which was only $9.10. In Berlin, the gross hourly fare Uber charged was $2.20, while the subsidy it paid out to drivers was $10.20 an hour. Uber burned through cash to “buy revenue”, in the words of the presentation."

https://www.theguardian.com/news/2022/jul/12/they-were-takin...

Uber kept fares artificially low while simultaneously paying high bonuses to drivers to build a massive network. After burning through roughly $30+ billion over its first decade, Uber then pivoted its business model by raising rider fares, increasing restaurant fees on Uber Eats, and cutting driver pay.

Basically, win market through subsidy -> establish monopoly -> increase price -> profit.