RFC8032 (section 8.7) states that IUF (Init, Update, Finish) should not be used in Ed25519 API:
Avoid signing large amounts of data at once (where "large" depends on the expected verifier). In particular, unless the underlying protocol does not require it, the receiver MUST buffer the entire message (or enough information to reconstruct it, e.g., compressed or encrypted version) to be verified.
This is needed because most of the time, it is unsafe to process unverified data, and verifying the signature makes a pass through the whole message, causing ultimately at least two passes through.
As an API consideration, this means that any Initialize Update Finalize (IFU) verification interface is prone to misuse.
It is a bad idea to modify Ed25519 or Ed448 signing to be able to create valid Ed25519/Ed448 signatures using an IUF interface with only constant buffering. Pretty much any error in such would cause catastrophic security failure.
Why? What implications does it have?