In my honest opinion, rooting a phone is half the reason I have android over iPhone. There is so much you can do with a rooted phone. I don't think it is the service providers right or privilege to tell you what you may or may not do with the data and phone that you pay them for. I understand that rooting voids the warranty, and that I assume risk once rooted, but the benefits far outweigh any detractors.
As far as backup apps, I have been using Titanium Backup pro for over three years now, since I rooted my first android. (the HTC Hero, which was considered one of the high end devices at the time... LOL)! It is simple, effective, and well proven to backup, restore, and freeze bloat. It is a wonderful tool for those that use it. YMMV, and good luck!