If one applies an electric field to a conductor, then the electrons inside it will start moving around, until the field is balanced out to 0. It is said in Griffiths’ “Intro to E&M” that this happens almost instantaneously. In contrast, electrons in a wire under an electric field move painfully slowly. Why don’t they move from one part of the wire to another “almost instantaneously”? He does mention that there are collisions happening between electrons in a wire, which slows them down, but then why don’t these collisions slow down the process of field removal in a general conductor?
Also, he says that the source of EMF can be anything from, obviously, an electric field within a battery to a temperature gradient or a repeated crossbow shooting electrons. In the last two cases then, as it seems to me, there is no electric field caused by the source, so what is the source of an electric field that makes the electrons move across the $\textbf{entire}$ circuit?