"The Most Sentimental Man", a 1957 short story by Evelyn E. Smith, available at Project Gutenberg.
The earth is being evacuated, and Johnson has chosen to stay behind, alone on a deserted world:
The commander was still unconsciously pursuing the same train of thought. "It does seem incredible," he said in a burst of boyish candor that did not become him, for he was not that young, "that you'd want to stay alone on a whole planet. I mean to say—entirely alone.... There'll never be another ship, you know—at least not in your lifetime."
Johnson knew what the other man was thinking. If there'd been a woman with Johnson now, Clifford might have been able to understand a little better how the other could stick by his decision.
Johnson wriggled, as sweat oozed stickily down his back. "For God's sake," he said silently, "take your silly ship and get the hell off my planet." Aloud he said, "It's a good planet, a little worn-out but still in pretty good shape. Pity you can't trade in an old world like an old car, isn't it?"
"If it weren't so damned far from the center of things," the young man replied, defensively assuming the burden of all civilization, "we wouldn't abandon it. After all, we hate leaving the world on which we originated. But it's a long haul to Alpha Centauri—you know that—and a tremendously expensive one. Keeping up this place solely out of sentiment would be sheer waste—the people would never stand for the tax burden."
"A costly museum, yes," Johnson agreed.
How much longer were these dismal farewells going to continue? How much longer would the young man still feel the need to justify himself? "If only there were others fool enough—if only there were others with you.... But, even if anybody else'd be willing to cut himself off entirely from the rest of the civilized universe, the Earth won't support enough of a population to keep it running. Not according to our present living standards anyway.... Most of its resources are gone, you know—hardly any coal or oil left, and that's not worth digging for when there are better and cheaper fuels in the system."
They are all gone, and he has a planet to himself:
He settled back luxuriously on the worn cushions of his car. Even so little as twenty years before, it would have been impossible for him—for anyone—to stop his vehicle in the middle of Forty-second Street and Fifth Avenue purely to meditate. But it was his domain now. He could go in the wrong direction on one-way streets, stop wherever he pleased, drive as fast or as slowly as he would (and could, of course). If he wanted to do anything as vulgar as spit in the street, he could (but they were his streets now, not to be sullied) ... cross the roads without waiting for the lights to change (it would be a long, long wait if he did) ... go to sleep when he wanted, eat as many meals as he wanted whenever he chose.... He could go naked in hot weather and there'd be no one to raise an eyebrow, deface public buildings (except that they were private buildings now, his buildings), idle without the guilty feeling that there was always something better he could and should be doing ... even if there were not. There would be no more guilty feelings; without people and their knowledge there was no more guilt.
[. . . .]
No, the stars were for others. Johnson was not the first man in history who had wanted the Earth, but he had been the first man—and probably the last—who had actually been given it. And he was well content with his bargain.