Should I explain to the graduate admission committee why I am older than most prospective PhD students?
Such information would be relevant. The real trick would be to keep such a paragraph short and to the point. As such the question would be a good draft of such a section. I have two comments:

I would not start the second sentence with "as you know". If a committee member did not know, you make her or him feel ignorant. It is good to avoid invoking negative emotions in such a letter. Especially since leaving that part out does not change the meaning of the sentence.

It was not clear from the text whether it was the Bahai faith that prohibited it's members from going to university or whether it was the Iranian government that prohibited people with the Bahai religion to enter university.