since the hashes of all alphabetic passwords of length 14 or less are known. (I don't remember for which hashing algorithm.)

Are you seriously suggesting that the blackhats can call on a database/lookup table of 26^14 * 14+16 = 1.5 Zetabytes of storage for cracking passwords?

For reference, the best figure I can find for Google's storage total is 220 TB, which means that these blackhats would need 7 million times the infrastructure as Google to store this table. Even if 10:1 compression was possible, that's still 700.000 Googles hiding away on the internet somewhere.

Even if they compressed the data and held it on tape, they'd still need 1000+ of these all fully populated to hold it. And each of those 1000 systems would cost 7 digits to buy.

Yes, I've heard of rainbow tables, but they don't address the fundamental problem much.