Even Saruman thought to do this to spite Frodo and goad him into a fight. Why didn't Sauron invade the Shire and start killing Hobbits and perhaps sending Hobbit heads via messengers to various places in the West to try and cause Frodo and his Hobbit friends agony and perhaps goad them into heading back to the Shire to rescue their people? I mean, the mere vision of some bad stuff in the Shire nearly got Sam to turn back, what if they got actual news of Hobbits being massacred? If the Nazgul could get in, why couldn't other things get as far as Bree and into the area of the Shire and just batter the gate down? As far as I know, Sauron's forces held Moria, so it wasn't like the West held all passes through the Misty Mountains. Also, while Galadriel's Ring would keep the forces of Dol Guldor OUT of Lorien, I'm not sure how well it would go if the fight ended up in the open with the forces of Dul Goldor moving toward Moria with the intent to attack the Shire. Also, I would have thought that Mordor would have other interests in the region anyway. With Arnor fallen, Bree and the Shire were all that was in the way, at least more north and west of the Misty Mountains, of the Grey Havens. Take over those and that would mean the fall of a major Elf seaport (it seems that they keep sailing out of there to go to Valinor (could they not sail from other ports?).), not to mention meaning that Mordor controlled or could control all lands west of the Misty Mountains which would leave Rohan and Gondor pretty much doomed.