About this question
We know that to slow down password cracking in case a password database leak, passwords should be saved only in a hashed format. And not only that, but hashed with a strong and slow function with a possibility to vary the number of rounds.
Often algorithms like PBKDF2, bcrypt and scrypt are recommended for this, with bcrypt seemingly getting the loudest votes, e.g. here, here and here.
But what about the SHA256 and SHA512 based hashes implemented in at least glibc (description, specification) and used by default at least on some Linux distributions for regular login accounts? Is there some reason not to use them, or to otherwise prefer bcrypt over the SHA-2 based hashes?
Of course bcrypt is significantly older (1999) and thus more established, but the SHA-2 hashes are already nine years old by now (2007), and scrypt is even younger by a bit (2009), but still seems to be mentioned more often. Is it just an accepted practice, or is there some other reason? Are there any known weaknesses in the SHA-2 based hashes, or has anyone looked?