Sauron has winged beasts under his control as well, and he would see them coming on an Eagle from miles and miles away. It's a lot easier for a couple small hobbits to sneak into Mordor.
<< how did sauron get so damn powerful to make the ring in the first place? and if he's that powerful, why can't he make an even better ring or an equivalent one? and of course for the ladies, how many karat gold is that ring??? ah a good tale but it brings up so many questions >>
He was the Lieutenant of the previous Dark Lord, Morgoth for one 🙂 He can't make another one because he already forged most of his powers into the Ring. It can do a lot more than make you invisible...that is just what it does for a Hobbit. Put it in the hands of say, Gandalf, and you'd have a much different story. Put it in the hands of its Master, Sauron, and say buh-bye to Middle-earth. 🙂