Not really. The hard thing here is not the network transport but user interface.

If people can learn the Snapchat UX, they can learn some SMS text adventure style Uber.

People can be illiterate, dyslexic, inebriated, dumb or with poor command of the language. Good luck with free-text interface.

You'll pretty much would have had human operators over every interaction. That very much hinders the Uber-like growth of the service.

If you can support 95% of the market (with mechanical means), you can capture 95% of the market.

That wouldn't be 95% of market, more like 50-60%, and a strain to use even for those apt. Not everyone is an Infocom playing nerd.

Normal people use SMS just fine all the time.

Falling back to a human operator isn't that bad either: just charge people a little bit extra to talk to a human.

I don't think that Uber through SMS would be strong enough to compete with taxi services.

One of the core features that made me use Uber was the map - I could see where the driver is going and how far away is he. Also, the app is localised into language that I can understand and I can see the price upfront without having to worry about getting scammed. Recently I had to book a taxi over the phone at the end of the world (literally - Ushuaia) in a language that I can barely speak and the experience was rather stressful in comparison with using an app.

Seeing a price up front is just a different business model and localization could be easily handled with a setting on your account. Neither is tech-dependent, both could have worked over SMS too.

Real-time mapping would be tricker if that's really a killer feature for you.

Some real life traditional taxi services used to offer pre-agreed fixed fairs. But many of them were regulated away.

For Uber though there's the driver side experience as well as the customer side. I don't know if you could've made something seemless enough for drivers to use from an old feature phone

Drivers have a car. So they could have used a bigger device. Eg a laptop, or something with a touch screen.

Or a voice connection with an operator.