I disagree. There are plenty of apps out that do just that. I use GoSMS Pro as my SMS/MMS user app and it has the ability to backup SMS/MMS to local SD, a 'cloud', or DropBox. As well, many carriers will provide a solution for backing up phone contacts, SMS/MMS, call logs, documents, videos, photos, music, etc. as needed (YMMV). My carrier is Verizon and their Verizon Cloud is *very useful for backing up messages and call logs. HOWEVER, it does not find all the media files as the app only knows to look in pre-defined locations. See my previous post here for my suggestion on what and how to backup. Look on Play Store for apps that will backup your messages.