The TF was omitted from the table of contents, which makes sense if it were an interpolation or at least interpolated, but less so if it were something written to drum up interest in the Antiquities.
https://peterkirby.com/table-of-contents-josephus.html
It might also be mentioned that you could make a living as a story teller but not really as an author per se. Someone like Lucian of Samosata was in demand in elite circles for the performance of his works. Having a popular book could spread your name, but it would not provide its author an income on its own. The money (if you will) was in live entertainment.
In case anyone doesn't realize, the Antiquities was incredibly long, often boring, and not the kind of book that got someone a lot of invitations to perform. And that's fine because there was a whole other very old category of literature produced under a patron's support. In this case, a person named Epaphroditus was notable:
"I separated it into a set treatise by it self, with a beginning of its own, and its own conclusion. But in process of time, as usually happens to such as undertake great things, I grew weary, and went on slowly. It being a large subject, and a difficult thing to translate our history into a foreign, and to us, unaccustomed language. However, some persons there were, who desired to know our history, and so exhorted me to go on with it: and, above all the rest Epaphroditus, a man who is a lover of all kind of learning; but is principally delighted with the knowledge of history; and this on account of his having been himself concerned in great affairs, and many turns of fortune; and having shewn a wonderful vigor of an excellent nature, and an immoveable virtuous resolution in them all. I yielded to this man’s persuasions; who always excites such as have abilities in what is useful and acceptable, to join their endeavours with his."
Of course there were people interested in history, and parts of the text could possibly have been brought out for reading at times.
But with this passage on Jesus there is not enough there to get that kind of value out of it. The passage is too short to do that kind of work. If it were longer, it could perhaps satisfy curiosity and entertain listeners for an evening. But the passage doesn't fill that space. If this was why it was written, the author immediately forgot his purpose just a few words in.
It doesn't fill that kind of function. It does work as a little quotable creed-like statement from Josephus, which is the first known use of it, in Eusebius.