Do organizations have an ethical obligation to have a succession plan in place?
Ethical obligations have to do with things that firms ought to do for moral reasons. These are things like treating their employees well or not cheating their customers. Creating a succession plan is not an ethical issue.
A succession plan might be good from a business perspective. It can help to identify good candidates for promotion within the company. It can help to reduce the level of disruption that the firm feels when an important employee leaves. But none of these things create an ethical obligation. These are not moral issues; they are issues of what will be most likely to allow the firm to operate smoothly. Therefore, it may be economically beneficial to create a succession plan, but it is not an ethical obligation.