When you use something like Electrum to generate a brain wallet, the passphrase is the seed. From this seed, the app generates an unlimited number of addresses, public keys, and private keys that can be deterministically re-generated, given the passphrase. So in this case, you can have one "brain wallet" (the passphrase) but an unlimited number of public keys generated from that seed; and revealing any of these public keys should be perfectly safe. Right?
Could I choose my own passphrase to do that? I don't trust those randomly generated passphrases.
But I want to be able to use a passphrase to pull up my private key without using software that could become deprecated or non-standard overtime. I would like to be able to recall my passphrase 40 years from now, and the standard generator will pull up my offline savings account without worry.