I've written appointment reminder software that leverages one of Twilio's competitors (Signalwire) for delivery and they seem to do just fine in things like this. In testing use cases, I have to prove ownership of both sending and receiving phone number. They also require all SMS messaging campaigns to be registered as per FCC requirements. I know they filter it too, because when the FCC rule went into effect I hadn't received notification yet, and my first clue was everything suddenly showing up in the logs as being blocked.