All your comments are true but it is a solution to an undesirable situation. In my opinion, the need to call an extraordinary meeting would be as a last resort as you should be able to make decisions within the standard calendar of meetings. Alternatively, a required number of councillors could also call an extraordinary meeting....
As for the resignations, I would take the view that the chair would be chair until the next meeting and therefore would be able to accept resignations in between but that is my interpretation and I would automatically seek advice from the borough council on this matter if it arose.
All in all, if you have a council that cannot produce a chair, you would have to think that something is seriously wrong...