Should juries be present at trials?

In fictional portrayals of trials, the jury is often told to disregard certain statements. Also, interruptions in the form of objections are common. Wouldn't it be easier for the jury to be absent from the trial itself, then presented with all and only the admissible evidence and testimony afterward? In fact, the jury need not see the parties in question, nor even know their names. Wouldn't that eliminate the possibility of racial discrimination and other irrelevant judgments?