I never understood why they do this face-to-face thing.
A lot of the battle mental. If you make the other person flinch or get a nervous reaction out of them, it has catastrophic effects on their ability to fight. Working out, having a game plan and being conditioned and in shape is one thing, but guys who fight at these levels go beyond of what normal people are capable off, and so the mental becomes really important.
If you want to see this in action, check out Thompson v. Aleksander Emelianenko (Fedors brother) ;
https://www.youtube.com/watch?v=1PqUKgXusoY
What you can see is that Thompson tries to intimidate Emelianenko, but Aleksander is not phased at all. It gives creedence to the saying "small dogs bark the loudest".
Fedor himself is also very stoic and doesn't try to intimidate his opponents as he feels it is just a shorthand for being insecure.
For people like McGreggor, Muhammed Ali, and many others, it is an effective tactic. They get inside their opponents head, frustrate them and cloud their judgment, and those milliseconds is enough to lose you the fight.
But not everyone who trash talks or engage in these staredowns have the same motives. Some are just trolling, others are just trying to make publicity, but it IS an effective tool!