When a toddler looks in the cabinet for toys and finds poison, we find that as an issue. So, we put the poison up, and/or install a lock. The same goes for the dangers of teens. They aren't ready for some things of internet, including porn and cyber bulling. As parents, we use parental controls to limit access to xrated channels on our tv. It makes sense to limit content to internet connected devices that do the same. We don't need a formalized study to see what access to porn can do to a person. It's been documented many times.
My experience has been, at this point in a childs life, you need to have, or establish a good relationship with your child and help them understand that you are protecting them from harm that they don't fully understand yet. They need to understand this protection is a joint effort between you and them for their best interest.
Some may say this is overprotected parenting. Let's not go overboard here. I've seen so many uninvolved parents, which is far worse than overprotected. I've found the middle ground is the most effective. Add controls to obvious problem sites and apps. Watch remotely from time to time (as sathackr said, trust but verify). Then, periodically, sit down with your child to see how they are doing and how you can help do the right thing online.