Sauron's Girdle?

[Mankáno]

First, the girdle of Melian acted confusing the people that tried to pass through it and it worked by the power of Melian applied to a totally different environment. The forest of Region and Neldoreth were appropiate for that, Mordor wasn't.

Second, I am not sure if Sauron was as powerful as Melian. They were both Maia but that means very little because the difference in power of the maiar was big, Eonwe, Osse, Uinen, Arien and Melian were known to be much more powerful than the rest.

Sauron was the most powerful of Morgoth's servant but that doesn't mean he was as powerful as the main maiar and, as Morgoth, he had given up part of his power to the one ring and to his servants.

Third, I don't think Sauron would think that was necessary, in the first place, the access to Mordor was nearly impossible, there were only two entrances from the West, Cirith Ungo and the Morannon and both were heavily defended. Secondly, Sauron didn't know, and didn't expect they would try to enter Mordor and destroy the ring, he thought the danger he was facing was that one of the wise could use the ring to destroy him, he couldn't think (in his greedy mind) that someone would refuse the power and would simply try to destroy the ring.