You seem tacitly to be assuming that "the" solution of Maxwell's equations for the field of a point charge is that given by the so-called "retarded potential Green function." But to make this (admittedly common) assumption is to impose a boundary condition (at null infinity.)
Consider the simpler case of Newtonian gravity. This may be formulated in two ways: via action at a distance (which is non-local), and via a gravitational potential function subject to a Poisson equation (which is local) AND a boundary condition at infinity (which is non-local.)
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If you drop the boundary condition on the Newtonian potential function, then an arbitrary homogeneous solution may be added to it. And this arbitrariness makes the gradient of the Newtonian potential -- i.e., the gravitational "force" -- arbitrary. It can be annulled at a point.
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A purely local formulation of Newtonian gravity theory, then, leads naturally and inevitably to the Equivalence Principle. In such a theory, the notion of gravitational "force" is meaningless. This notion can only be recovered by adding a non-local "law" to the theory.
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