I would say that 3 out of the 5 had an agenda. Death is an agenda, life is an obligation.
Of course, I am not sure that any system which gave effect to Terri's desire to die would meet with your approval. Nonetheless, our system is a hybrid of the adversary and the "neutral". So, in Terri's case, there were 2 experts selected by the Petitioners, 2 by the Respondents and 1 by the Court. That is rather typical of such proceedings.
My experience as a lawyer is that I am generally more satisfied with the party-selected experts because you know where they are coming from. Obviously, a party is not going to proffer an expert that doesn't support their theory of the case. The court generally will use the so-called 'neutral' expert to compare and contrast the theories of the party-experts.
I realize you don't like the result in this case, but the system is actually a pretty good one. It exposes all views and gives the trier of fact contrary expert views to help it (court or jury) weigh one against the other.
I personally would not want the whole group to be so-called "neutral" experts. They tend to be selected blindly and you can't be sure that they will really air both sides of the case fairly. So, don't throw the baby out with the wash water. Keep in mind this is just one case where you don't like the result, but don't give up on a very good system.