Really, there isn't. People ask too often, "Can I appear by phone?" Mediators and attorneys both should ask, "Why would you want to?" It can't be because you want to increase the odds of making a sound decision or of having the other side make one.
We have 5 senses. Sometimes we need inputs from more than one to accurately assess a situation. The same is true for mediation as it is for just about anything else. And how can we get the real flavor of a dynamic exchange of information, ideas, suggestions and proposals if we are only getting one sensory input. We all know that reading a deposition hardly imparts the subtleties, and even sometime misses major revelations or tones. Having someone listen-in to the mediation is always a less than ideal development.
If someone is unable to be there, it should be rescheduled. If someone doesn't want to be there, and it is your client, you have to ask, "Does this person have the perspective I want them to have?" Being present allows a problem solver to say "I am taking this seriously and I am going to give this my / our best shot, so you should as well, before we have no choice but to let a jury or judge decide." It also let's the decision maker respond to the things that are unspoken, or perhaps misinterpreted by others who convey the information to the decision maker in some other city, inevitably with distractions. Avoiding these inefficiencies or inadequacies increases the soundness of the ultimate decision. And the key to resolution may ultimately hinge on the other side's appreciation for their adversary being there, listening, and working on getting something accomplished. Think about it, if it is hard for you to negotiate beyond your preferred zone, does it help if the other side isn't there?
If it is the other side who doesn't want to attend, you should consider trying to get someone higher up to attend in person to take the process, and what you have to add to the analysis and problem solving, seriously. Otherwise, what you say may just fall on deaf ears.
While attending by phone can be adequate in some cases, there really is no substitute for being there. It can also keep the mediator's charges lower than if everyone has to wait for all of the calling back and forth to be accomplished.