Just to clarify when I wrote just because it existed (earth Government and the form it took) when Federation Membership was granted, doesn't mean that same Government still exists. I have already stated several times in posts today that I think some form of local Earth government must be there, but we have no idea of its scope and size and responsibility. It could be a vast government or it could have extremely limited powers and responsibility. We don't know.
We know that at no time after ENT has Earth Government been shown to take care of Earth security. At least Earth security from external forces. Be it V'Ger, the Probe, or alien infiltration. In all those cases its either been shown to be starfleet, or Starfleet/ Federation President making those calls.