To expand on this for any future readers, there's been attempts in the past, success one's that have tried to demonstrate the security of a brain wallet, with a large randomly generated password, and they were never cracked. However, the problem with brain wallets is how you generate them, a lot of users will probably go to a website to generate it, and that introduces a number of attack vectors, which you wouldn't have if you generated your seed via a offline computer. You've first got to trust the website, then you've got to make sure there's no man in the middle attacks going on, and ultimately you have to either download the code or run it via the internet through your web browser.
Also, it's worth mentioning just because something is open source, it doesn't mean it's secure or isn't malicious.
How would you explain some brainwallet passwords complicated enough like a bitcoin address or a long hex string which have been cracked already and people did use them with amounts as big as hundreds of bitcoins?
Brain wallet concept is a high risk method in general.
For security and privacy sake, it's better to generate several addresses with separate private keys, that way you could sever the links between wallets.
