For example, if there are two point charges (both positive) on a plane, and a test charge is placed closer to one point charge than the other, the test charge would incur some sort of E-field. Whereas, if the same scenario is recreated with plates instead of point charges, the test charge would end up with no net E-field.
I would say that the answer has to do with how the electrostatic field from these two kinds of sources (points and plates) depends on the distance from them. With a point source, you have a divergent field that decays with a 1/r^2 dependence. A line source (that is, an infinitely long line source) has a field that decays with a 1/r dependence. A plate (infinitely long and infinitely wide) has no dependence on distance. That seems unphysical (and it is) but it is the consequence of postulating a charge that is infinite in extent (and therefore has infinite total charge). To put it in very loose terms, you can't get "far away" from an infinitely large plate. Another way of saying it is that the field from an infinite charged plate has no divergence.
When two sources are involved, we can solve for the total field simply by superposition. Since both line and point sources have fields that depend on distance, the fields cancel only at specific locations. But since the field from an infinite plate has no location dependence, the cancellation is perfect in the entire space between them (assuming the two plates are parallel). Note, of course, that if the test charge is located not between the two plates but on one side of them, the total of the two fields would add instead of subtract, and you would get a net field.
Of course, if the plates are finite in extent, then this no longer strictly holds. But if the gap between the plates is small compared to their lateral extent, the approximation can still be a very good one.
I hope this helps.
Matt
Your question is not self-consistent by nature, simply because if you assume two positive charges (+ Q & +Q lying anywhere in the space, in order to be consistent; you MUST consider the presence of some negative neutralization charge distribution or a single point charge (- 2Q), located somewhere, being either forced or simply induced on some finite size conductive or dielectric surface.
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