He did not need to and he preferred not to fight for himself.
Denethor, who had a good understanding of the Dark Lord, since he engaged in communication and personal mental combat with him for some time, pointed out the following when Pippin feared that Sauron was come himself to Gondor:
‘Nay, not yet, Master Peregrin! He will not come save only to triumph over me when all is won. He uses others as his weapons. So do all great lords, if they are wise, Master Halfling. Or why should I sit here in my tower and think, and watch, and wait, spending even my sons? For I can still wield a brand.’
This is reflected throughout the history of Middle Earth. Going backward, in the War of the Last Alliance, Sauron only came out after the Alliance had defeated his armies in the Battle of Dagorlad and laid siege to Barad-Dur itself, a siege that lasted for seven years. In other words, he had no choice but to fight, on the very slopes of Orodruin:
‘I was the herald of Gil-galad and marched with his host. I was at the Battle of Dagorlad before the Black Gate of Mordor, where we had the mastery: for the Spear of Gil-galad and the Sword of Elendil, Aiglos and Narsil, none could withstand. I beheld the last combat on the slopes of Orodruin, where Gil-galad died, and Elendil fell, and Narsil broke beneath him; but Sauron himself was overthrown, and Isildur cut the Ring from his hand with the hilt-shard of his father's sword, and took it for his own.’
(Council of Elrond)
He did not fight with the Numenoreans, when he directed them to conquer Valinor:
For Sauron himself was filled with great fear at the wrath of the Valar, and the doom that Eru laid upon sea and land. It was greater far than aught he had looked for, hoping only for the death of the Númenóreans and the defeat of their proud king. And Sauron, sitting in his black seat in the midst of the Temple, had laughed when he heard the trumpets of Ar-Pharazôn sounding for battle; and again he had laughed when he heard the thunder of the storm; and a third time, even as he laughed at his own thought, thinking what he would do now in the world, being rid of the Edain for ever, he was taken in the midst of his mirth, and his seat and his temple fell into the abyss.
(Akallabeth)
He refused to fight the Numenoreans before that:
And Sauron came. Even from his mighty tower of Barad-dûr he came, and made no offer of battle. For he perceived that the power and majesty of the Kings of the Sea surpassed all rumour of them, so that he could not trust even the greatest of his servants to withstand them; and he saw not his time yet to work his will with the Dúnedain.
Although he did submit to being their prisoner, so he could corrupt them in person, with the One Ring. Going back to the First Age, Sauron's name is notably absent from all the major battles, despite being the lieutenant of Morgoth; the one time we know he engaged in personal combat, he was defeated by a girl and her dog.
Why did he have this preference, aside from it being the smart thing to do? We can reasonably speculate it was for similar reasons as Morgoth: by becoming truly incarnate in the world, he did introduce the possibility of him experiencing pain and physical death, even if it was unlikely. And death (not merely separation from the Ring) did diminish Sauron:
It was thus that Sauron appeared in this shape. It is mythologically supposed that when this shape was ‘real’, that is a physical actuality in the physical world and not a vision transferred from mind to mind, it took some time to build up. It was then destructible like other physical organisms. But that of course did not destroy the spirit, nor dismiss it from the world to which it was bound until the end. After the battle with Gilgalad and Elendil, Sauron took a long while to re-build, longer than he had done after the Downfall of Númenor (I suppose because each building-up used up some of the inherent energy of the spirit, which might be called the ‘will’ or the effective link between the indestructible mind and being and the realization of its imagination). The impossibility of re-building after the destruction of the Ring, is sufficiently clear ‘mythologically’ in the present book.
(Letters)
Dispersing his power and will throughout the world (Morgoth and Sauron both did this, though Morgoth on a much grander scale and incarnating himself into a physical form made Morgoth know fear.
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.
(Quenta Silmarillion)
Just like Sauron, Morgoth could never be truly "killed"; his spirit is still out there and he will re-incarnate himself someday. But nevertheless, becoming incarnate makes you fear death. So to some extent, Sauron probably had become a coward, as well.
But more than that, Sauron did not need to intercede himself at any time during the War of the Ring. As we saw, he would fight if he absolutely had to. But he didn't. Sauron's victory in the War of the Ring was essentially inevitable: all he had to fear as that someone else would claim and use the Ring (he did not consider that the might destroy it.)
Consider what Denethor saw in the Palantir:
But against the Power that now arises there is no victory. To this City only the first finger of its hand has yet been stretched. All the East is moving.
(The Pyre of Denethor)
You might argue that Denethor was crazy at the time. Well, no; Gandalf agreed:
‘My lords,’ said Gandalf, ‘listen to the words of the Steward of Gondor before he died: You may triumph on the fields of the Pelennor for a day, but against the Power that has now arisen there is no victory. I do not bid you despair, as he did, but to ponder the truth in these words.
‘The Stones of Seeing do not lie, and not even the Lord of Barad-dûr can make them do so. He can, maybe, by his will choose what things shall be seen by weaker minds, or cause them to mistake the meaning of what they see. Nonetheless it cannot be doubted that when Denethor saw great forces arrayed against him in Mordor, and more still being gathered, he saw that which truly is.
‘Hardly has our strength sufficed to beat off the first great assault. The next will be greater. This war then is without final hope, as Denethor perceived. Victory cannot be achieved by arms, whether you sit here to endure siege after siege, or march out to be overwhelmed beyond the River. You have only a choice of evils; and prudence would counsel you to strengthen such strong places as you have, and there await the onset; for so shall the time before your end be made a little longer.’
(The Last Debate)
Consider that in the first assault, described as only a finger of the Dark Lord's might, Sauron very nearly overthrew the entire west of Middle-Earth. Gondor was burning and only barely saved; in Mirkwood there is "long battle" and "great ruin of fire; "grievous harm" is done to Lthe borders of Lorien, where the text does say Sauron himself would have had to come because of Galadriel's power; King Brand and King Dain were killed, and Erebor was besieged. It really didn't matter to Sauron if Saruman betrayed him, or if he lost a few battles here and there. He could afford to be patient. Indeed, all might have been lost in the first assault: the whole point of Aragorn challenging Sauron in the Palantir was to trick him into striking early, before he was ready. And they still nearly lost.
So then we have another part of your question:
And if he had personally, physically confronted Frodo (I know, he had no idea where Frodo was, but bear with me - this is a hypothetical scenario), it is hard to imagine Frodo coming out of the encounter in one piece, let alone in possession of the Ring.
In fact, Tolkien says that Sauron would have had to physically confront Frodo if he had not destroyed the Ring - but Frodo would have probably understood he could not stop Sauron from taking the Ring from him and would have cast himself into the fire.
When Sauron was aware of the seizure of the Ring his one hope was in its power: that the claimant would be unable to relinquish it until Sauron had time to deal with him. Frodo too would then probably, if not attacked, have had to take the same way: cast himself with the Ring into the abyss.
(Letters)
Tolkien then goes on to suggest what might have happened if the Ringwraiths could have confronted Frodo: they would have pretended to obey him, lured him out of Orodruin, and then waited for Sauron:
In any case a confrontation of Frodo and Sauron would soon have taken place, if the Ring was intact. Its result was inevitable. Frodo would have been utterly overthrown: crushed to dust, or preserved in torment as a gibbering slave.
(Letters)
So Sauron would have confronted Frodo personally. Recall that he did also apparently torture Gollum personally.