You've also accurately captured the dynamic process of a criminal trial. The problem is that you don't form the intent as defence counsel to introduce a document into evidence. In fact, it is inadmissible in evidence up until the point where the witness, number one, says something unexpected on the stand, and number two, then doubles down on it in cross examination even after being confronted with the document.
I think it may be contrary to the message that Parliament wants to send to complainants that we're going to require defence counsel to bring these applications on the assumption that all complainants will lie and then double down on it. I think that is not the message you want to send.
The way to address the issue that you've raised, which is that eventually it might all come to it, is to recognize that the time at which it will all come to admitting into evidence is in the middle of trial, and the process should be flexible and streamlined enough to deal with the fact that it's a mid-trial application.