The app provides various official services, among them a digitized version of the "yellow sheet" a legal guardian has to fill out for a woman to be able to leave the country. (https://www.rt.com/news/women-tracking-saudi-arabia-359/ from 2012 describes this particular system, the app apparently integrates it with more digital services).
The alternative isn't freedom of movement, it's having to get a signature on paper and potentially personal appearance of the legal guardian, which is harder to get (this includes: forge) than a button click on a website. As a remedy for that reduced trust in the system, it sends an SMS - to the very same device.
There are activists in Saudi Arabia (see for example https://twitter.com/monaeltahawy/status/1095360734798721025) who see value in that type of app because the degree of automation it brings makes it easier to leave the country without supervision (e.g. by stealing the legal guardian's phone).