A private key is as large as 1024 which, as stated above, is a much larger quantity than the number of atoms in the universe. Trying to extract the signature from the document is futile, and attempts can be easily detected. This is primarily what allows non-repudiation. Because a document can only be signed by someone holding the genuine private key, one can be assured the real owner of the key signed the document, if her public key correctly verifies her signature. Third, handwritten signatures change over time.
Some people never sign their names the same way twice.
This could lead to false negative or false positive identification. In either case, a digital signature would not cause the same difficulty. A digital signature never changes, until it is revoked in the event of a lost or stolen key. An exact match is required for all authentication, and there is no guesswork on the part of the validator. But on the other hand, Bob has no way of knowing for certain that Alice is the person who sent the letter.