An easement by necessity is not something that a grantor grants. It is a grant from the court that unlocks property based on the common ownership of the property before it was subdivided and the intent of the grantor, absent an explicit grant for ingress/egress. If an easement was granted when the property was divided and bequeathed, it would be a granted easement by the grantor (likely the estate of the deceased) . That will not change whether they use the easement or not. Is that easement articulated on subsequent deeds of the neighbor's property?
Now if there is a granted easement that unlocks the property, there could be no easement by necessity or by implication granted by a court across your land because there must be no alternative for ingress/egress to the landlocked property. In this case you say that there is an easement to the public road.
Can you say that they can no longer your driveway? Sure you can. Will it hold up in a court challenge, that's just a guess and the outcome will be based on the full facts of the case should it go to court.
I will say that you can't just shut off access one day. You will need to notify the "would be dominant estates" of your intentions and allow them time to respond.
I suggest that you consult an attorney and have them carry this forward if that is the direction you want to go.

