So obviously there's nothing in the movie to answer the question about Starfleet planetary defenses or lack thereof. It could be a plot hole but I'll give the writers the benefit of the doubt and say that the codes extracted from Pike allowed the Narada to bypass them completely; otherwise why was it so important that Nero get them, and why is that scene shown to the audience?
However your assertation that "the majority of Starfleet's fleet had recently been destroyed by Nero" is in fact incorrect. When the alert comes in to Starfleet Academy during the inquiry of Kirk's Kobayashi Maru test it is explicitly stated that the cadets must mobilize to respond to the Narada threatening Vulcan because the majority of the fleet was occupied in the Laurentian system (http://en.memory-alpha.org/wiki/Laurentian_system). If you'll recall the argument between Kirk and Spock that ends up with Kirk being exiled from the Enterprise is over whether or not they should go join the fleet and get ready to respond, or follow the Narada directly to Earth alone.
So the ships responding to Vulcan's distress call are destroyed, the "bulk of the fleet" is regrouping before a counterattack, and I think it's safe to assume the other Federation ships are off doing the things they are known for doing in the 23rd century and are unable to make it to Earth in time.
Of course the real reason is most likely because it makes a more effective film if Kirk and crew save the Earth rather than showing someone at a terminal calibrating planetary defenses :-)