This property can be advantageous for some uses, such as dissemination of announcements and public keys, where the more copies distributed the better. But it is unsuitable for many other applications. Consider electronic replacements for all the written or oral commitments that are to some extent personally or commercially sensitive. In such cases the proliferation of certified copies could facilitate improper uses like blackmail or industrial espionage. The recipient of such a commitment should of course be able to ensure that the issuer cannot later disavow it - but the recipient should also be unable to show the commitment to anyone else without the issuer's consent.
Undeniable signatures are well suited to such applications.
An undeniable signature, like a digital signature, is a number issued by a signer that depends on the signer's public key and the message signed. Unlike a digital signature, however, an undeniable signature cannot be verified without the signer's cooperation. The validity of an undeniable signature can be ascertained by anyone issuing a challenge to the signer and testing the signer's response. If the test is successful, there is an exponentially high probability that the signature is valid.