“The country is well served by having a press who is there and can keep a check on any president,” said Ari Fleischer, who as George W. Bush’s longtime press secretary often clashed with journalists. “Even on Sept. 11, we recognized the important need for the country of having a pool travel with the president.”

The broader idea, advocates argue, is that the president’s whereabouts ought to be recorded — for public reassurance and the historical record, and so the president has reporters nearby to quickly communicate with the public in a crisis.

And if Mr. Trump rejects the decades-old practice of the “pool,” where journalists follow the president even to the most banal engagements, will he adhere to other traditions such as news conferences and press briefings that are meant to inform the public about matters of greater import, but are not mandated by law?

“My friends who cover the White House say that the Obama administration was probably the most closed administration that they have ever tried to cover,” said Sally Quinn, the longtime chronicler of Washington media and society. “They ain’t seen nothing yet.”

The challenge now for the Washington press corps may be convincing the broader public that these decades-old protocols still matter even in an age of instant communication tools like Twitter that bypass traditional news outlets, and in the face of a groundswell of public skepticism toward the establishment press, whose supposed coziness with the White House was one of Mr. Trump’s favorite talking points at rallies.