Hi Fajar, in a certain way all Accountabilities are optional as the Role filler himself defines how to energize his/her Roles and Accountabilities.
Governance is there to create clarity so if this Role is the one to take the ongoing action then this can be added as an Accountability for this Role. This makes clear to everybody who is accountable for it.
F.E. a Role can have the Accountability: Sending end of Year thank you cards to all customers. This Accountability will only be energized during a small period of the year.
In your example I wonder what the Objection was. If somebody has an Accountability by default he or she decides how and when to energize this Accountability. So it is not about the action but about making clear who has the accountability if this is needed.
Hope this helps.