But combined with hash trees they can be used for many messages and then become a fairly efficient digital signature scheme.

Public-key cryptography can also be used for implementing digital signature schemes.

The security of this signature scheme is based on an NP-hard mathematical problem.

Therefore, the signature schemes based on multivariate equations systems are considered to be quantum resistant.

Especially for systems with very small resources this signature scheme may be interesting (smart card).

Niederreiter can be used to construct a digital signature scheme.

The signature scheme is correct in the sense that the verifier will always accept genuine signatures.

However, combined with hash trees, a single key could be used for many messages, making this a fairly efficient digital signature scheme.

Most signature schemes are quite different, using only a digest, which as you mention is quite different.

The fact that other signature schemes don't work that way is, therefore, a little beside the point, in my view.