Since $V=Ed$, why doesn't the electric potential increase when length of the wire increases. $d$ increases right? Is it because the battery only pushes the electrons from one terminal to the other and not from one end of wire to the other end?

Or is it because that electric field is a conservative field and that work done does not depend on path taken?

EDIT(copied from one of the comments):can we use the following explanation: In an electric field, the electric potential(in the case of positive charge moving away from a positive charge) is line integral of $E.dr
$ . Since line integral does not change with the path taken, every path will give you the same potential