There's a reason I said the scene works on paper. It fulfills a lot of valuable functions for filling us in early on Barrett's passion for his cause, how he sees what he's doing (or wants it to be perceived), how Shinra underlings see what they're doing, and how people on the plate see people living down below. I also think, perhaps wishfully, that it gives us a sense of the act he puts on (Barrett knows he can be intimidating and is willing to use that to his advantage, even though we already know by this point that he's not going to beat innocent people up).
But the execution sucks in a lot of different ways that weren't necessary to get those points above across, and most of them are tied to how exaggerated everything is. Keep in mind that Barrett and his friends blew up a power plant an hour ago, are wanted by the law, and are trying to keep a low profile, even as they carry weapons around a train loaded with people who just saw the horrible aftermath of the explosion.
If Barrett's just trying to stick up for Avalance without seeming like a card-carrying member (since they are wanted by the law, and he wants to keep his operations secret), why does he say his initial lines defending Avalanche as if he's acting for a PR video? Why do the Shinra employees sound like they came from Metal Wolf Chaos? If Barrett is intimidating, and those employees are the sort of people who fear the Midgar slums and the people living there, why does Barrett have to (or think he has to) take a step forward and growl in their faces if he wants to frighten them? Why do they have to recoil in fear so hard one of them is putting his hand in front of his face as if he's about to get punched? Why do they literally applaud the manager's speech as they sit in a public subway car? Does (low profile!) Barrett have to kick a bench in a subway car to show he's upset with his inability to get through to them?
It's a sloppy scene in execution, and the sloppy exaggerations in it enhance the stereotypes surrounding Barrett's character. It doesn't help that all this happens before we meet Marlene, which is the first step towards grounding him as an actual human being.