the-art-of-moi- I think there is a greater danger of not allowing the teen to have a lock. Any teen can go to the local public library and access the internet there. If they want unfiltered internet, they can go to the local internet cafe. If the parents don’t allow them even a lock on their door to allow them to get dressed in their rooms, that shows a lack of trust. When you don’t trust someone, they give you a reason not to trust them.
On the other hand, if parents make filtered wi-fi readily available, and get a list that cannot be deleted of any site accessed over the network, the parents can get a general idea of where their kid is up to without infringing on their teens privacy.