Maybe the one where you flagged down a car on the street, but you could always call to book a taxi and those companies worked exactly like Uber — over the phone, because it was the pre–app era.
So no, the old taxi companies did NOT work "exactly like" Uber.
Quoted for truth. I still take taxis from time to time if there’s no wait at a taxi stand at an airport or building. I noticed in places like Las Vegas things seem better now, there’s flat rates and everyone has touchscreen payment terminals in the passenger area. I remember pre-Uber occasionally getting cab drivers that would take suboptimal routes like getting on the freeway to drive up the meter.
Not in my country they didn’t. Booking or no booking, taxis did whatever they wanted. More often than not your booked taxi just wouldn’t turn up and you wouldn’t know until well after you needed it.