“But for most of the scenarios mentioned above you might not rely on external sms gateways or APIs because they should also work if your internet goes out.”
An alarm that texts you through a cloud API dies with your internet connection. A Raspberry Pi, a cheap Huawei 3G dongle and a SIM card keep working when the router doesn’t. Gammu does the hard part. Twilio sells this as a service. Here it’s a weekend project and a prepaid SIM.