Matt Schlapp, who oversaw federal affairs for Koch Industries during President George W. Bush’s second term and is now the chairman of the American Conservative Union, said the most lasting legacy of the Koch network will likely be its funding of a large network of think tanks and universities.

“I give the Kochs and their network high marks on understanding that if they don’t change hearts and minds and build institutions that can educate people in the nonprofit world then the world will drift to the left, the government will continue to grow,” Mr. Schlapp said.

He said their direct impact on politics was less pronounced. “The best judgment you can give it is mixed,” he said. Part of that mixed legacy is linked to the rise of Mr. Trump. Some prominent alumni of Koch-funded organizations do hold high-ranking positions in the Trump administration. But the Kochs’ approach to governance, beyond curbing business regulations and cutting taxes, has often been sidelined, if not rejected outright, by the Republican Party under President Trump, who dismissed the brothers as “a total joke” last year.

Trevor Potter, a former chairman of the Federal Election Commission and the current president of the Campaign Legal Center, a watchdog group, said the true Koch legacy was having “diminished our democracy.”

“The Kochs changed two things. First, the system went from transparent spending to secret spending,” Mr. Potter said. “The second was they were an important part of the wave of billionaires who took campaign spending to an entirely different level in American politics.”

Both developments, he said, gave average Americans a deep sense of disenfranchisement.

‘A Historical Power Player’

Parts of the Koch network have at one point touched on nearly every facet of the conservative movement. There have been separate organizations for outreach to Latinos (the LIBRE Initiative), veterans (Concerned Veterans for America), younger voters (Generation Opportunity) and older voters (60 Plus Association), for instance. A national political group, Americans for Prosperity, established outposts in the majority of states across the country.

“David Koch helped design and implement the center-right, free enterprise, activist wing of the political spectrum,” said Scott Reed, the senior political strategist of the United States Chamber of Commerce. “And he became a historical power player .”