Why does a strong system like the one in Brave New World, exile people who don't conform to social rules?
The reason for this is that the system is actually not strong. It seems to be strong on the outside because it can manipulate its people so thoroughly, but it really is weak.
The system is apparently weak because it cannot tolerate dissent. It clearly fears that people like Helmholtz or even Bernard will inspire other people to start thinking and then to rebel. We can see this sort of thing in the real world. Strong systems like the US allow people to rebel because we know that the vast majority of people like the system and will not joint the rebels. By contrast, systems like that of China are so worried that their people will rebel that they do not allow any dissent or anything that even sounds like dissent.
The World State does not have a strong system. It has an oppressive system that is capable of doing what it wants to the people. But its system is not strong enough to withstand dissent. This is why it exiles people who don't conform.