The benefit of having a succession plan is that the firm will transition as smoothly as possible from one leader to the next.
If a firm has no succession plan, it will flounder for a longer period of time when one leader leaves. The next leader will have to be selected without any prior planning. That new leader will come in and have to jump straight in to the new job without any transition period in which he or she learns from the outgoing leader. The new leader will have to be building relationships "on the fly."
These factors show why a succession plan is a good thing to have. A succession plan, well executed, allows the firm to transition smoothly from one leader to the next and have little or no lost time while the new leader learns on the job.