Indeed, Elder Bednar quotes five prophets at the beginning of his talk to improve his ethos. Each quote adds a drop of strength to his argument that Church members should "flood"the world with the gospel.
As members of the Church, we revere the prophets. So hearing Elder Bednar quote Brigham Young, "Every discovery in science and art . . . has been given by direct revelation from God," strongly affects us.

Brigham Young? He was, like, the prophet after Joseph Smith.
That means he's old.
That means he knew about technology long before our time.
That means prophets know stuff, and that Elder Bednar knows that prophets know stuff.
That means we should listen to Elder Bednar.
This is essentially what goes through our minds as we hear that quote from Brigham Young. Drip. And then again when we hear the voice of Spencer W. Kimball. Drip. And again as we watch our beloved Gordon B. Hinckley. Drip.
Socrates makes reference to leaders in his argument, too. He recounts how he personally heard Pericles, a prominent political figure, speak (p. 40). Then, he alludes to the writings of a known philosopher, Anaxagorus (p. 49). They must have been figures of import; otherwise, Socrates wouldn't have mentioned them.
At first it appears that this isn't as effective as Elder Bednar's drip-drip-drip strategy at the beginning of his talk. Perhaps, though, it is more effective for Socrates' audience. By mentioning these famous leaders throughout his argument, Socrates reminds his audience that, "Hey. I've listened to Pericles. Drip. I've studied other philosophers. Drip. I know what's up."
Thus, this rhetorical strategy of testimony helps strengthen the ethos (and therefore the arguments) of both Elder Bednar and Socrates.