My wife just had to get a new phone shipped to her because of this Backup Assistant mess.
First of all, she set it up initially (I didn't see her do it or else i would have screamed NOOOOOOO).
It kept trying to backup pictures and was freezing her gallery and phone to the point where only a battery pull would fix it.
Did a factory reset - skipped the BUA and I made sure this was the case this time. The VZW ROM checked for a subscription anyway and even though nothing was checked or activated, the behavior was the same!!
She took it to VZW who apparently signed us up for phone insurance at $6.99 a month without our knowledge or consent. In this case, it helped us because she's getting a new phone overnighted. On a 3rd factory reset, I think I was able to clear the behavior, but want her to get a new phone.
All pictures that were taken with the phone are GONE. All photos sent via S-BEAM are GONE. Verizon has no record of these photos being backed up, and the factory reset wiped them from the device (even though her camera app was set to store things to the SD card). The fact that the Verizon backup app is what caused this mess has me furious with them. It's not the phone's fault.
Bottom line: BUA and BUA+ has been a total nightmare for her. As others suggested, use Google for contacts, and use any of the cloud storage services for pictures (Dropbox, Google Drive, Box, Google+, Flickr, Picasa, Facebook, etc). You might also consider using IFTTT.com to set up some automation tasks to move files around (example, if post a picture to Instagram, move to Flickr or Dropbox.