Where did you get this idea?

First, I think Deism pre-Darwin more closely resembles atheism post-Darwin than Deism post-Darwin, and so it's more informative to modern readers to use the more similar reference point. Second, I don't see strong reason to believe the self-identification of historical figures in cases where the truth would damage their reputation. Franklin, in particular, gives many examples of bending his public conduct to maximize his reputation.

For example, I take this line from his autobiography to be more significant than the one where he calls himself a thorough Deist:

and farther, that my indiscrete disputations about religion began to make me pointed at with horror by good people as an infidel or atheist.

As for:

even thought organized religions, such as Christianity, were necessary to maintain morality amongst the common people.

I don't think he thought organized effort was just for the common people:

My arguments perverted some others, particularly Collins and Ralph; but, each of them having afterwards wrong'd me greatly without the least compunction, and recollecting Keith's conduct towards me (who was another freethinker), and my own towards Vernon and Miss Read, which at times gave me great trouble, I began to suspect that this doctrine, tho' it might be true, was not very useful.

I get the sense he would have happily attended church if the local pastors were as good at other-improvement as he was at self-improvement, but they weren't, and so going would be a misspent hour. He still paid the subscription for them his whole life (as far as I can tell, as another reputation-preserving measure), and the Junto is probably the closest thing to a religious organization that he actively participated in.