In the US, sure. But if you travel internationally as I do, Lyft isn't even Outside the US yet while Uber is in almost 100 countries. There's no comparison.
"It is also this setup that also allows Uber to pay what their critics say is less than their ‘fair share’ of tax – Uber pays no VAT and, last year, only paid £411,000 in Corporation Tax."
https://www.londonreconnections.com/2017/understanding-uber-...
I also traveled domestically and overseas a ton (four years with Accenture on the road constantly) and remember a pre-Uber world. Shudder. While you are right that I can theoretically go with multiple services domestically in the US, I'd still go with a single one to ensure easy accounting, and when dealing with overseas travel, it is a no-brainer.