If trial by jury is so important, why should our society allow a defendant to reject a jury trial and elect to have a trial to a judge?
Jury trials are important, but our right to jury trials is more important. When accused of a crime, we have a right to a fair trial, and a jury is a part of limits placed on the government so that our freedom is not taken away unfairly or arbitrarily. But since it is our right, we also have the freedom to waive that right (or any other, for that matter), particularly if we feel it is in our best interest. A judge will usually tell us not to waive a right to a jury trial, but we still can if we wish to.
Jury trials are important to our society because they are meant to protect defendants from arbitrary government actions. Since the whole point of having jury trials is to protect the defendant, it makes sense that the defendant (and not the prosecution) would be able to waive the right to a trial by jury.
A trial before a judge (and not a jury) is not necessarily unjust. However, injustice would be much more easily done if there were no jury trials. Therefore, it is extremely important that jury trials be the norm, but it is not important that they be the only possibility.
So long as it is the defendant's choice to have a jury trial or not, the benefit to society is preserved and it does not really matter if the defendant chooses a bench trial rather than a jury trial.