Why is the obvious solution being missed here? In an adversarial trial, there are usually a minimum of three parties: defendant, complaintant, and court. As is

Why is the obvious solution being missed here? In an adversarial trial, there are usually a minimum of three parties: defendant, complaintant, and court. As is often the case in criminal and civil trials, both non-court parties bring their own witnesses and experts to testify. It seems wise to me to also regularly have a court appointed neutral expert(s) along with experts for the other parties.