It is the way of Dark Lords, especially those in Middle-earth, to remain safely behind and secure in their place of power while using others as tools and weapons. Sauron's boss, Morgoth, was the same way. From The Silmarillion:
In Angband Morgoth forged for himself a great crown of iron, and he called himself King of the World... that crown he never took from his head, though its weight became a deadly weariness. Never but once only did he depart for a while secretly from his domain in the North; seldom indeed did he leave the deep places of his fortress, but governed his armies from his northern throne. And once only also did he himself wield weapon, while his realm lasted.
For now, more than in the days of Utumno ere his pride was humbled, his hatred devoured him, and in the domination of his servants and the inspiring of them with lust of evil he spent his spirit.
On that one occasion when Morgoth did wield a weapon, things didn't go exactly as he had hoped. He fought Fingolfin, High King of the Noldor, but only reluctantly. From The Silmarillion:
And Morgoth came. That was the last time in those wars that he passed the doors of his stronghold, and it is said that he took not the challenge willingly; for though his might was greatest of all things in this world, alone of the Valar he knew fear. But he could not now deny the challenge before the face of his captains; for the rocks rang with the shrill music of Fingolfin's horn, and his voice came keen and clear down into the depths of Angband; and Fingolfin named Morgoth craven, and lord of slaves.
Many times Morgoth essayed to smite him, and each time Fingolfin leaped away, as a lightning shoots from under a dark cloud; and he wounded Morgoth with seven wounds, and seven times Morgoth gave a cry of anguish, whereat the hosts of Angband fell upon their faces in dismay.
While Morgoth was victorious, he did not come out of the battle looking good; he was wounded by a mere elf, and never again came forth. Given that Morgoth was Sauron's teacher, we can imagine that Sauron got the message - don't fight your own battles!
Nonetheless, we do see Sauron engaging in combat himself a few times throughout the legendarium.
In the tale of Beren and Lúthien in The Silmarillion:
Therefore [Sauron] took upon himself the form of a werewolf, and made himself the mightiest that had yet walked the world; and he came forth to win the passage of the bridge.
Then Huan sprang. There befell the battle of Huan and Wolf-Sauron, and the howls and baying echoed in the hills, and the waters on the walls of Ered Wethrin across the valley heard it afar and were dismayed.
But no wizardry nor spell, neither fang nor venom, nor devil's art nor beast-strength, could overthrow Huan of Valinor; and he took his foe by the throat and pinned him down. Then Sauron shifted shape, from wolf to serpent, and from monster to his own accustomed form; but he could not elude the grip of Huan without forsaking his body utterly.
Sauron was humiliated in battle against a dog.
We know little of Sauron's actions during the War of Wrath that brought down Morgoth; but we do know that he fled from battle, and refused to return to the good, for fear of humiliation.
We know little as well of Sauron's actions during the second age, beyond teaching the elves the craft of Ring-making. We do know that he felt unable to defeat the Númenóreans in open battle, so he surrendered to them and corrupted Númenor from within.
We do know that Sauron fought personally against Gil-Galad and Elendil in the war of the Last Alliance, and that he was defeated and overthrown by them. That was when he lost the Ring.
So throughout the Legendarium, we see again and again, when Dark Lords fight directly, they lose, or they are humiliated.
Sauron had no desire to fight anyone. He took delight in commanding others to do things, not doing them himself. He would only enter battle personally as a last resort, when no other avenue is open to him. The battle at the Black Gate was not such a last resort. That was simply the destruction of an arrogant fool coming with too little force.