Yes the accused does have a choice whether to be tried by a jury or not. They can plead guilty .
That trial by jury has worked in England and in the US for over 700 years I would claim as a success.
Personally I would rather face a body of people who are like me to decide my fate in a case than face a lone judge or a court of appointed magistrates.
All legal systems can have problems and a jury is probably the least predictable method, but the defendant is pressumed innocent until proved guilty in our system. Over systems where no jury is used often seem to seek to secure an already presumed guilt.