A mistake that lawyers sometimes make is failing to ask for what they want. If they do want an evaluation they can ask for it when they hire the neutral. There are processes variously known as neutral evaluation, non-binding arbitration, or early case assessment which are designed specifically for this purpose. They can be used independently or they can be combined with mediation.
I was once hired to give a neutral evaluation in a commercial real estate case. The parties told me at the outset that while they were interested in exploring settlement they were really interested in my opinion on the merits. So we conducted a mediation that included a neutral evaluation. Not only did this meet their needs, the evaluation was given in a confidential setting and could not be used as evidence if they did not settle.
The point is that both parties wanted the process to be evaluative. It was not a situation where one party was expecting the mediator to be evaluative and the other party wanted the mediator to refrain from doing so.
When parties hire a mediator, they need to be of the same mind about the process. Otherwise the result will be like splitting a steak with your partner when one of you likes it rare and the other likes it well done. Somebody is going to get indigestion!