Imagine a court case where an argument for a defendant could be made that is judged to give them only a very slight increased chance of being found innocent, but would take a disproportionately large amount of time to prove. I'm wondering how a judge would handle these cases, can a judge curtail the defendant's right to defend himself on the grounds that it costs too much to add a day's worth of trials for such a minor proof?
So lets say there are two examples.
Someone claims to have not known "john doe" but is later proven that they know each other. The prossecution uses this as evidence of the individual lying to discredit the witness, with the witness being only a minor witness to begin with, say one of 2-3 people colobrating an allabie. The Witness explains that he is horrible with names and so didn't recognize the name of someone he has semi-regular contact with despite knowing the individual well. The witness could help to increase his credibility by parading dozens of character witnesses in front of the court to prove his difficulty with names is a known and common issue and just the witness probably wasn't lying, but it's allot of effort to increase the credibility of a non-major witness.
A defendant is put on trial and the prosecution points out that the defendant was googling or asking questions that seem somewhat related to the crime, suggesting the defendant was preparing for the crime. The defendant says he was researching the information for some story he was planning to write, but the prosecution points out the defendant hasn't written any drafts of this supposed story down and implies there is no story and that's a flimsy justification for his search history. To help increase his credibility the defendant could spend the next half a day explaining all the plot points in his planned story in detail, how the research he did was relevant to specific plot points, and generally provide an extensive enough narrative that it seems likely this story had been being built on for some time as claimed and isn't a fictional story; but it's still a long time to provide only minor increase in credibility.
Does a judge have the right to say that the benefit to the defendant is deemed so minor that it's not worth wasting the time and expense required to present this defense. Of does the judge have to allow any defense, no mater how tedious, if the defendant claims it would help their cause?