The 2nd was initially more to assure the states the means to protect themselves against encroachment by the central government (and thereby dissuade such encroachment), a concern that was within vivid living memory for the framers, and was of particular concern to skeptics of the centralization that the Constitution represented compared to the Articles of Confederation.

Like all of the Bill of Rights, it was about constraining the Federal government, not the Podunksville Police.