Those are the big cases. In between are many offences that are either way offences. There are 370 categories of such offences in English law, applicable in England and Wales. The public case for retaining a broad base for jury trial is that it allows citizens to participate in the legal process.
Jury trial is popular and adds to the legal system's credibility.
It reduces those elements of the legal process in which only lawyers are involved. The point of principle is that jury trial is fundamental to our system of criminal justice. The state brings the case against its own citizen, and must prove it. It is an axiom of our law that the state does not prove it in front of its own appointees. If cases are serious, they must be proved in front of your fellow citizens.