I checked the Bible, the Bhagavad-Gita and the Koran, and God never uses the expression “Having said that.”
Why everyone else seems to be saying it is one of the mysteries of existence.
And if “Not having said that,” makes no sense, what are we really saying by its opposite?
If it means anything, it’s a backtrack phrase, really–a slight retreat on one front so as to consolidate the overall import of the statement.
On the other hand, there’s a guido TV weatherman in Orlando who uses “having said that” as a verbal segue bridging tonight’s lows and tomorrow’s highs with the seven day forecast. No semantic content at all: “Having said that, I now say this.”
I suspect that the phrase in question makes people feel important or authoritative when they say it, and that’s part of its recent popularity. As if: I’m so important and informative even the modulations of my opinions are worth discussion.