Yes, it's true that a judge needs to weigh the information about a motion for continuance. If crucial people, like the judge, attorneys, witnesses, and prosecutors become sick or disabled, that's a "no-brainer".
But in the case of new evidence coming up, the judge needs to look closely at this and grant the request if it's likely to provide a fairer trial.
Also, the judge has to consider whether the continuance is a stalling or manipulative move. He has to decide if this will slow down the effort to have a speedy trial for the defendant.
It can be a tricky decision for the judge, but if he has any doubts, I think he should error on the side of caution to do all he can to provide a fair trial.