I've read your explanation of this problem several times in the past and only now I figured out (I think) the problem you are pointing out. This seems to be substance of your argument, as I understood it:
The computational expense of a brute-force attack against a hash is the lesser of (hash length, text length). Well-known hash functions (md5, sha*) are optimized for large blocks of text, which leads to two properties: 1) they are made fast 2) them being fast is not a problem - if the text is long the strength against the brute-force attack is determined by the hash length which is very respectable for sha256 or even sha512.
However, the passwords themselves are small - the typical password is 8 characters and assuming 7 bits per character you're looking at search space of 56 bit, at which point it doesn't matter if your hash is 64, 128 or 512 bit because your strength is 56 bit. The search space can be further reduced by accounting fr various password selection biases, for example phonetic bias, tack-number-at-the-end bias, keyboard layout bias and so on.
To deal with small search spaces we need algorithmically slow hash functions - their slowness is not a problem because text is small, but it's a benefit against the brute-force attack.
Yes. Think also of it this way: poor user password selection (and here we mean "ugh&8eat" is a weak password) sabotages the complexity of the attack, and adaptive hashing (like SCrypt) fixes that problem algorithmically.
Which is how it should work. Users shouldn't have to pick absurd passwords when the computer can do a better job of obscuring their password.
(Note: "them being fast", for "them" in SHA1, SHA256, etc, is not even considered a "problem"; it's considered a "huge feature", because these things are protecting individual data packets. It just happens that this primitive by itself is not useful for protecting passwords.)
But we force users to choose obscure passwords to discourage dictionary attacks (so I thought) not to protect them in case our dbs are hacked. A computer may be able to obscure a password better than the average user but at the end of the day the user still has to commit that password to memory, which may be why people stick with the same simple passwords to begin with.
Even a small change in the message will (with an extremely high probability of 1-10^(-154)) result in a different hash, which will usually look completely different just like two unrelated random numbers do.