Is signing a message hash a valid replacement for blind signature?
Wouldn't this algorithm replace the blind signature implementation as described in Wikipedia in every case?


No, because hashing is a deterministic algorithm. Let M be Alice's message, and $H(\cdot)$ be the hash function.

In your algorithm, Alice passes H(M) to Bob, who can store H(M) for later reference. This way, Bob effectively creates a database of message hashes signed by him, as well as the ID of the user who asked for Bob's signature. Let $D = \{\langle H(M_1), ID_1 \rangle, \langle H(M_2), ID_2 \rangle, \ldots \}$ be this database.

On seeing a message-signature pair $(M, \sigma)$, Bob hashes M to H(M), and searches D for H(M). If H(m) is found, Bob can easily recover the ID of the user. Hence, this method does not blind the identity of the user.