According to the Wikipedia article for Blind Signatures:
Blind signatures can also be used to provide unlinkability, which prevents the signer from linking the blinded message it signs to a later un-blinded version that it may be called upon to verify.
The principle of unlinkability exists (among other reasons) to protect the anonymity of the message's author. Imagine that 4 people each give a blinded message to the signer, which the signer provides signatures for. At some later date one of the messages is revealed. The signature should prove that A) the message is un-altered (integrity), and B) it is one of the original 4 messages (authenticity), but it should not be able to tell which of the original 4 it is (anonymity).
If you used "signing a hash" as a form of Blind Signature, then the signer (or an attacker recording their network traffic) could remember which hash came from which person, and then once the full message is revealed, you can compute its hash, compare it to the hashes that were submitted, and know which author wrote it, thus de-anonymizing the author.
Some applications or use-cases may not care about unlinkability, in which case signing a hash is a fine way to do a Blind Signature. But if you do, then this scheme is no good. For example, Blind Signatures are commonly used in election systems in which the inability to trace a revealed ballot back to the person who cast it is a requirement of the system.