Five years ago, Travis Kalanick was so confident that Uber Technologies Inc.’s rides would prompt people to leave their cars at home that he told a tech conference: “If every car in San Francisco was Ubered there would be no traffic.”

Today, a mounting collection of studies shows the opposite: Far from easing traffic, Uber and its main rival Lyft Inc. are adding to congestion in numerous U.S. downtowns.

Officials...