Can I disable private browsing on my child's iPad and iPhone?

I was very happy wih the parental restrictions on the iPhone/ iPad until my child pointed out the private browsing feature. I've resolved this issue on the MacBook by using external software; however, the only external software I can find would require my child to use a different browser. We go for transparency, not control, so these "blocking" apps arent what I want anyway. I'd like my Child to surf freely, but be aware that we will know where he goes. That way, he can learn to discern between appropriate and non appropriate sites on his own, and anything worrisome can be discussed.

This seems a glaring omission on a piles part; is there some way to disable PBS altogether, or an app that simply logs built does not require use of a second rate

Browser that blocks sites?

I do not want my child to feel he has to sacrifice browsing experience just because he is a child, that would breed resentment but I do want our policy of transparency to continue. It's obviously working well, as he came himself to tell me about the problem.

Thanks everyone!