Mediation requires the trust and confidence of both sides. Opposing counsel are adversarial, they don't trust each other. Mediators have access to confidential information from both sides which facilitates settlement, attorneys do not. Both sides have hidden agendas. The mediator has none.
Mediators are neutral, attorneys are advocates.
Attempts to be both an adversary and a neutral creates serious conflicts in the eyes of your client. Mediators' core competency is bringing about resolution. Attorneys core competency is advocacy and protection of clients' rights and remedies. Statistically, the vast majority of cases settle at mediation. Also, this reason assumes that all cases settle during the first round of negotiations, which they don't.