Although none of these characters could be taken as the kernel of truth to that tale, they might have lent to the motivation to historicize that tale; to claim accounts that it had actually happened here in the real world and very recently. Remember how the story has Jesus telling his disciples that none of them would even taste of death before he returned? That’s why they embellished this story so soon. They really really wanted to believe it. That’s how faith works. That’s why they’re still waiting for him now —even though he’s a couple thousand years late. Now I the reason he hasn’t returned yet is that he was never here in the first place.
Remember that the primal impulse behind the fabrication of the Gospel Jesus was the apocalyptic urgency/certainty that Jesus was really arrived in the "End of Times". To claim that he had manifested himself in the form of the various Josephian figures (at least to these figures in Josephus who resemble so strongly to the Gospel Jesus, after the fabrication of the latter) could give hope to the same author(s) of a such claim, hope that Jesus was really arrived in the "end times".
About this eager apocalypticism as primal impulse for the euhemerization of Jesus, so Paul-Louis Couchoud (quoted from his Le Dieu Jésus):
In Paul, the redemptive death of Jesus is in the timeless. It is a divine act constantly continued up to the next Manifestation of Jesus. In the Epistle to the Hebrews it took place, on the contrary, in time, only once and for all (hapax). It will never repeat itself. The author demands, with all his great stern soul, that apostates who, out of cowardice, have renounced the redemption they owe to the blood of Christ, can no longer be redeemed. It is in the uncompromising rigor of the first days of persecution. With this decision of penitential interest, the Redemption of men becomes a realized fact. It is expressed in the aorist, the historical tense. This is of great consequence for the origin of the gospels. Where in history to fix the death-resurrection of Jesus? It was natural to place it at the end of time, just before the Christophanies granted to Peter, to the Twelve, to the five hundred brothers of Jerusalem. It will be difficult now to keep it above the ground. Why wouldn't it take place on earth? The author of Hebrews, an idealist if ever there was one, does not quite reach this conclusion. For him, the priestly sacrifice of Jesus, temporal as it is, is not at all an event of this world. It took place outside the world and Christians must leave the world if they want to encounter the Crucifix: "Jesus suffered outside the city gate to sanctify the people. Let us therefore also go out of the camp to go to him, bearing his reproach, for we have no lasting city down here” (13:12). Soon a more realistic piety will know in this lower world the precise place that moistened the blood of the Redeemer.
(my bold)
The Christian apocalypticism of Hebrews, the idea that Jesus suffered only one time in the past, and in the recent past (and NOT in the remote past, pace Wells), is the true impulse that moved the Earliest Evangelist to write a story by "seeing" his invented Jesus in the actions of some Josephian figures.
Otherwise, without that Christian apocalypticism (as exemplified optimally by Hebrews), there would be not interest at all about the instantiation of the mythical Jesus in the various Josephian figures.