Let the court (and the jury) hear it. The prosecution can present it and the defense can impugn it.
Not the same - if you can't cross-examine the witness. What if he had a beef with the man he named as the perp ??? What if he was a proven liar ??? Can't do that without the opportunity to ask questions of the witness.
Other witnesses called to reput the declaration probably would not be able to enter it into testimony because it would be hearsay ...
Right. Still hearsay.
Dying declaration: The jury heard it?
Direct testimony relating to the character and reliability of a dead witness is "hearsay"?
Okay, then that's another mess for our filthy "justice" system to clean up.