"City of Yesterday", a short story by Terry Carr which was also the answer to the old question Short story about a pilot who is integral to a space ship that attacks planets; first published in If, December 1967, available at the Internet Archive. You may have read it in one of these compilations.
The pilot stretched in his chair, flexed muscles in his arms and hands. "How long was I asleep?" he asked.
Eight months, seventeen days plus," said Charles.
That long! A quarter-oredit for sleep time that would give him over two months on his term of service, leaving him . . . less than a year. Earth standard. J-1001011
felt his heart speed up momentarily, before Chaiies's nerve-implants detected and corrected it. The pilot had been in service for nearly seven subjective years. Adding objective sleep time, it came out to over nineteen years. The sleep periods, during
Hardin Drive travel between star systems, ate up his service term easily for him . . . but then he rememhered, as he always did, that the objective time was still the same, that his parents, whoever and wherever they were, would be getting older at objective time rate on some planet.
Nineteen years. They should still be alive, he thought. He remembered them from his childhood, on a planet where colors had been real rather than dyed or light-tinted,
where winds had blown fresh and night had fallen with the regular revolution of the planet. He had had a name there not a binary number — Henry, or Hendrick, or
Henried; he couldn’t quite remember. When the Control machines had come for him he had been ten years old, old enough to know his own name, but they had erased it. They had had to clear his memory for the masses of minute data he'd need for service, so the machines had stored his personal memories in neat patterns of microenergy,
waiting for his release.
Human battle pilots were needed because their nervous systems were more
efficient than any microminiaturized computer of the same size and mass;
it was as simple as that. And human pilots were expendable where costly mechanization wouldn't be.