Before the Black Gate

[The Barrow-Wight]

In other words, the desolation was like a work of art to Sauron, and he loved the way it looked so much that he couldn't bear to clean it up. Kind of like the criminal who takes a souvenier from the scene of a crime knowing that it might lead to his capture at a later date. It seems dumb in hindsight, but the crook never imagines someone will search his pockets.

[Sharkû]

The terrain in front of the gate only provided very little cover, barely enough for three hobbits, not enough for Aragorn's army. At a point where the Black Gate is even less possible to assail because of Sauron's strength, I doubt he'd need to bother with the threat of 10 soldiers lying in wait of his storey-high fortress. As for spies, it's hard enough to hide a whole Haradrim army anyway, the enemy might as well see them and despair, an effect to which the landscape itself can contribute.
Moreover, the obstacles there seems to be at least somewhat recently formed, or at least that's possible with ash dunes, rocks (from eruptions?), and shallow pools. Such a frontyard would be hard to maintain, but maybe Sauron did do so at a time when he perceived himself as more vulnerable.

[Thulorongil]

I agree, Sharkû. All the igneous activity, landslides, and whatever else might logically have been going on in the area would make the landscape almost constantly change. Why spend time constantly clearing up over there when Sauron could be training his armies, building new wings onto his fortress, planning attacks, or gloating? Especially when there was almost no chance at all in his mind of someone using the area to attack him? Also, why spend time cleaning it up when he could use it, like Theron said, to even more thoroughly discourage anyone and everyone. So many things that the "bad guys" in Tolkien's writing do are based on frightening and intimidating the enemy. (And, come to think of it, frightening and intimidating their allies, too.)