Earlier quoted context omitted.
When it comes to AC (even discontinuous DC), closed loops are not necessary for current flow. A basic example is a capacitor, which can permit current while it builds up an electric field between is plates. A related example is an antenna, where AC radiates energy that can vibrate electrons in a far away antenna. (Radio telescopes are proof an antenna doesn't need a ground or a closed circuit to receive.)
Closed loops ("circuits") are part of the paradigm, so yes they are necessary at the level of abstraction we generally analyze electronics in. Sure if you came from Pluto with a metal sphere teeming with excess electrons, they would disburse themselves on our planet and never return home, but that isn't circuit analysis! For example, the current into one terminal of a capacitor does equal the current out of the other…
The realm of electrodynamics is pretty interesting, and it's where seemingly basic concepts like electric potential begin to fail -- it becomes path-dependent!