Are state borders necessary if there are no restrictions on the movement of people?

To me, state borders help define citizenship in order to help the state define the group that particular state is responsible for governing over. State borders create terms such as "citizenship." But if people have the choice of free movement from one state to another, are borders really necessary and how would their citizenship change from state to state? Wouldn't the freedom to move from state to state create a global citizen, one that is not bound by a particular state? Would there be a standard requirement as to how one would earn the citizenship of the other state and if this is so, who would decide what these standards are and wouldn't the standards have to be the same for all states? This decree of citizenship by choice leads me to question whether or not it would be possible to have a concept such as international citizenship, where people may move as they choose but are allowed to hold as many citizenships of their choice. Perhaps people can have a choice as to what their main citizenship is, but if residing in a place after a standard duration of time would automatically change their main citizenship. Would having a standard rule for all states to follow in determining citizenship make governing the body of people more efficient or would this standard create more problems? State borders and the concept of international citizenship would seem workable if there were no measurements on the success of states creating equality and lessening incentives for concentrated migration of persons, which if were to happen would trigger fear and a reaction of a heightened sense on the importance of citizenship and belonging in order to protect ones rights.