NEW YORK—Ash Barty, the No. 1 seed at the U.S. Open, watched on match point as her opponent’s backhand sailed long on Thursday, prompting the familiar sound of a linesman yelling, “Out!” There was no line judge, however. The call was a recording, triggered after an advanced system of cameras known as “Hawk-Eye Live” tracked the ball until it landed out of bounds. For the first time, the tennis major has installed electronic line-calling on every court, replacing human judges who were responsible for determining whether, say, a serve traveling at 140 mph touched a line the width of a ruler. “I didn’t even notice that,” said Chris Foglia, 48, a surgeon from New York, as he and his wife Melissa watched Simona Halep take on Kristina Kucova on Wednesday. “I have very mixed feelings—I like the human element.” But, a few minutes later, he acknowledged how difficult it was …