I've read a dozen studies so far that indicate Uber increases traffic and congestion in cities it operates in. Quite a lot, actually. Increasing commute times by 40% or more in some of the studies. Venture capital is paying people to idle around the city, clogging the roads. It's a sort of denial of service attack.
"Uber and Lyft Admit They're Making Traffic Worse"
This is the normal outcome of more people going to more places. Ridesharing definitely increased the total amount of people taking cars that didn't before from a lack of options, but that's minor in terms of general population growth.
Traffic always increases over time, that's a natural thing that cities need to plan for. It's great motivation to build public transportation instead of complaining about Uber helping people get around.
You didn't answer the core point. People don't sit at home if there are no taxis. That's never happened. And if cyclists take cars now, it's probably because it's safer to do so than riding around traffic. These aren't bad things.
"Uber and Lyft Admit They're Making Traffic Worse"
https://www.citylab.com/transportation/2019/08/uber-lyft-tra...