If someone is caught in the act of committing a felony, the case should be ready for trial within a few days (less then a week). If a person is arrested on a warrant, considerable time has already been spent on the case. At the point the person is arrested on a warrant, the prosecution should be ready for trial and the judge signing the warrant should have enough belief in the person's guilt to justify keeping them in jail a few days. The length of time the person spends in jail prior to trial would then be determined by the defense.
First this keeps the person from fleeing or not showing up for the trial. Secondly and more importantly, it prevents the person from victimizing others while out awaiting trial.