A brain wallet is pretty much useless if the Blockchain is declared illegal information. That's even the most likely scenario of a goverment crackdown - CP links encoded into it ring a bell?
Blockchain stored in nations where it's not illegal, everyone else uses it the same way Bitcoin Wallet for Android does it, where it only requests balances and relevant info for the addresses it's keeping track of. No need to keep copies of the illegal information. Done.
Someone would still have to store it. It's not like some part of the blockchain could be omitted by everybody.
Besides, it would be pretty baseless to make something like an accounting ledger illegal.
They could argue it's not the accounting ledger that's illegal but the excess information that is already. And because there are no methods available to prevent somebody to store more illegal information in it it can be declared illegal to posses the block chain.
You have to keep in mind to follow how a bureaucrat would think in case he is supposed to "do something about that".
It is clear that such a thing would be difficult to enforce, and somebody somewhere would still store the blockchain regardless of the potential consequences (a lot of people actually). But it would sure be a pain for anybody with a company to openly use Bitcoin. Think about how pot prohibition works.