Imām Ibn Ḥajar al-‘Asqalānī quotes the following in his Fatḥ al-Bārī Sharḥ Ṣaḥīḥ al-Bukhārī:

“Ibn al-Mājishūn* said: Only the people of the town where the witnessing occurs are obliged [to fast] unless it is established by the Caliph (al-Imām al Azam). In such a case, all the people are obliged [to fast], because all the towns with respect to him (the Caliph) are as one town, since his verdict is binding upon everyone.”
[Translated by Shaykh ‘Abdullah bin Hamid ‘Ali]

*“Abu Marwan ‘Abd al-Malik ibn ‘Abd al-‘Aziz ibn ‘Abd Allah ibn Abi Salama al-Majishun (r) (d. 212) the sea of knowledge, a Jurisprudent and Mufti of Madina, a contemporary of Malik more than his actual student, he studied mostly under his father, then with Malik and others. Whenever al-Shafi‘i rehearsed Fiqh with him, people would not understand them because they spoke the desert Arabic of Hudhayl and Kalb. Suhnun and Ibn Habib praised him lavishly and preferred him to most of Malik’s companions.”
[The Four Imams and their Schools, Shaykh Gibril Fouad Haddad, Muslim Academic Trust, 2007, p. 148]

[NB: The relied upon opinion in the Hanbali, Hanafi and Maliki Madhabs is global sighting of the moon. The main point made here by Ibn al-Mājishūn is that if the Caliph announces the beginning of Ramadan (or indeed for ‘Eid), then all will be obliged to accept his decision since his verdict is binding upon everyone.
Having an orthodox Caliph ruling us would solve the chaos caused every Ramadan and ‘Eid by a certain kingdom]

[See for Hanbali Madhhab: Muwaffaq al-Din and Shams al-Din ibn Qudama, al-Mughni (Beirut: Dar al-Fikr, n.d.), 3:10-13]
[See for Hanafi Madhab: Muhammad Amin “Ibn Abidin”, Hashiya Radd al-Muhtar (Beirut: Dar al-Fikr, 1415/1995), 2:432-433]
[See for Maliki Madhab: Mubarak bin ‘Ali al-Ahsa’i, Tashil al-Masalik ila Hidaya al-Salik ila Madhhab al-Imam Malik, ‘Abdul Hamid bin Mubarak, ed. (Riyadh: Maktaba al-Imam al-Shafi’i, 1416/1995), 3:783]