There is nothing wrong with SMS. Let's reverse engineer, and redesign the whole network as if to protect communication between two people.
1) Let's make it a point-to-point communication network where there's a salt known only to the sender and receiver and the phone numbers are encrypted. This prevents spoofing and/or spam.
2) the gateway itself only has one instance, and that instance is secured by at least 256 bit encryption, and is physically isolated from other equipment and tampering. To ensure that endpoint device theft isn't an issue, offline mode is disabled.
3) A one-time phone number can be used to send SMS to users outside of this secure environment restricting the original phone number from being harvested or spoofed.
4) Phone number blocks all SMS's for numbers not on contact list.
Now, we forward engineer about 20 years, scale it using enteprise and off-the-shelf equipment and call it Snapchat (and hack off the group messaging feature). It's now more secure than President Obama's Blackberry, but still isn't impervious to jealous girlfriends, wives, and screen shots.