By using SMS for auth, you are opening yourself to many threats.

For example any user can spam signup on your page with random phone numbers, leading to mass SMS span on behalf of your app. That will lead you to spend quite a lot on SMS API, and can potentially mark your app as spammer.

Also consider people without phone number, or international users whom cannot receive SMS or receive them with large delay. Or users travelling, but roaming disable, so they can't receive SMS. SMS channel itself is not considered secure for _serious applications_ that require high security. 

If you app does not deal with money, it is probably okay.