I think you're 100% right, and there was even natural experiment confirming this when Uber (and Lyft) left Austin temporarily. Basically the city council wanted rideshare drivers to do City background checks. There was a public referendum, and Uber/Lyft said they'd leave if it passed. Then it passed, and they left. Pretty much overnight there were 3-4 Austin-centric Uber competitors. Riders and drivers just switched apps. Colloquially, people would even still say "get an Uber" while using these other apps.
Eventually this was superceded by a Texas law, and Uber/Lyft came back, but the rideshare apocalypse that was predicted never came to be because there are very few barriers to entry in this market: build a relatively simple app, paste up some fliers or billboards advertising your new company to drivers and riders, and you're in business.
Admittedly, Austin has more ambitious app coders than most other random cities, so it might not be literally overnight like it was here, but it won't take that long for somebody to do the same in the rest of the country/world. On the other hand, those places likely won't lose Lyft at the same time like Austin did, so it may be a wash.
Eventually this was superceded by a Texas law, and Uber/Lyft came back, but the rideshare apocalypse that was predicted never came to be because there are very few barriers to entry in this market: build a relatively simple app, paste up some fliers or billboards advertising your new company to drivers and riders, and you're in business.
Admittedly, Austin has more ambitious app coders than most other random cities, so it might not be literally overnight like it was here, but it won't take that long for somebody to do the same in the rest of the country/world. On the other hand, those places likely won't lose Lyft at the same time like Austin did, so it may be a wash.