Spend time: figure out what app, download it (possibly on data roaming), make a new account, use app once, be stuck wuth data breaches forever, and good luck figuring out which one is tracking you all the time and running your battery to the ground.
Uber is not an angel, but at least with one app we have a lot of people pointing out privacy violations. With two (say, Lyft in US cities), there's some choice. If Uber really fails and the taxis end up running the streets again, I don't see any real pressure to make good ride hail / pay apps.
I don't travel frequently. When I do, install the app at home and then uninstall on return. So they can't track me when I am not using them. I understand it's not for everybody.
Google for it and then stand around reading the reviews to figure out which is the best one, you mean. And sign up for a new account and everything with the new app. By that time I'm already on my way to my hotel with Uber.
Expect Austin to occur elsewhere (Uber and Lyft leaving due to local regulation, and competitors filling the void).