Why does a lowered dielectric constant cause RNA/DNA precipitation in ethanol precipitation?
For ethanol precipitations [...] shouldn't the water-phosphate attraction be increased in magnitude by the same ratio as that by which the phosphate-cation in increased in magnitude?


The interaction between negatively charged nucleic acid and positively charged counter ions is an ion:ion interaction. The interaction between ions and water is an ion:dipole interaction.


  An argument based on the relative higher amounts of cations and ethanol, and lower in water, would make sense in increasing the likelihood of a cation-phosphate bond over a water-phosphate hydrogen bond, but then any mention of the dielectric constant in explaining ethanol precipitation seems entirely superfluous.


The presence of water between ions of opposite charge diminishes their long-range attraction (the dielectric constant is related to how well solvated ions are "shielded" by the oriented dipoles of the solvent). 
Ion:dipole interactions are short range and rely on the dipole to be properly oriented. Adding ethanol to the aqueous DNA solution does not make the ion:dipole interactions of water with ions stronger. In contrast, it does make the ionic interactions stronger because ethanol is less effective in shielding charges than water.

It is important to compare dielectric constants of water and ethanol because both molecules are uncharged and polar (and capable of ion:dipole interactions), but water is the better solvent for ionic compounds for the reasons discussed above.


  [from comments] I don't understand why [we add] ethanol. Ion-dipole interactions and ion-ion interactions are both interactions based on charge and should thus both follow Coulomb's law. Ion-dipole interactions are certainly weaker, and hence shorter range, but that doesn't seem like it should exempt them from Coulomb's law. Dipole orientation is something I hadn't considered.


A dipole has a positive and a negative partial charge that add up to zero. Imagine you are the cation that interacts with a dipole. When the dipole is near you, the negative partial charge will be right next to you, and there will be a large attraction. The positive partial charge will be a bit further, so there is a smaller repulsion. Overall, it adds up to an attractive force. Now move the dipole away from you, maybe by a factor of 10. Now, the positive charge will attract much less, and be at approximately the same distance as the negative charge, so the repulsion and attraction will almost cancel out.

Take a look at pentavalentcarbon's answer to a question on intermolecular interactions. There is a nice table with the dependence of interaction strength on distance.