This question has come from John, in Australia

It is not necessary to have an independent chairperson unless a) your rules dictate it; or, b) it is the custom of your organisation.
Even if it is the custom, there is no need necessarily.
If however there are any contentious issues coming up at the AGM, it may be wise to have independent chairperson.

Independent chairs are great whenever there is conflict, or totally opposing factions, or where the chair is so embroiled in an issue, that they cannot impartially chair the meeting.

I am hired to be an independent chair and it is nearly always when there is conflict. Sometimes, it is because the elected chair is lacking in confidence or feel that they do not have the skills to chair a meeting. Chairing a meeting is most certainly a skill, particularly when there is conflict.