Monday’s announcement that GE is replacing its chairman, Jeff Immelt, brought me back to a little-noticed moment at the end of the John F. Kennedy Library Foundation’s dinner last month honoring President Obama with its “Profile in Courage Award.”

Following Mr. Obama’s speech, the chairman of the foundation, superlawyer Kenneth Feinberg, concluded the program with the words, “Ladies and Gentlemen, I thank President Obama for those comments. I thank the ambassador, Caroline Kennedy, for her efforts in helping us prepare and implement this great evening today. And I particularly thank Jeff Immelt, and General Electric, for their leadership in providing this, this evening.”

Quite an achievement for a corporate executive, Mr. Immelt, in a crowd that included not only Mr. Obama and a raft of Kennedys but also Vice President Biden and Senator Warren, to get the final, emphatic thank you.

How many other people are there who not only socialize with Kennedys and Mr. Obama, but also, simultaneously, serve as an adviser to President Trump?

Mr. Immelt played golf with Mr. Trump and has visited him at the White House. The executive claims credit (or blame, depending on how you see it) for having talked Mr. Trump into starring in the “Apprentice” television show when GE owned NBC. The role helped eventually propel Mr. Trump to the presidency.

GE has a long and sometimes even glorious tradition of involvement in American politics that dates back well before Mr. Immelt took over the company. This struck me first when I had the chance to visit President Reagan’s ranch in the hills above Santa Barbara, California. The house itself is modest, with the exception of the kitchen, which is furnished with top-of-the-line GE appliances, a dividend of Reagan’s years from 1954 to 1962 as a General Electric spokesman. Thomas W. Evans elaborates that story in his book “The Education of Ronald Reagan: The General Electric Years and the Untold Story of His Conversion to Conservatism.”

GE’s corporate politics have shifted leftward in the years since Reagan, as evidenced by Mr. Immelt’s tweet lambasting Mr. Trump’s decision to withdraw from the Paris climate agreement.

The company’s active involvement in public affairs can cut both ways. At best, as in GE’s relationship with Reagan, politically involved companies can help educate politicians about the benefits of capitalism and the barriers created by taxes and regulations. At worst, the relationships can degenerate into cronyism, as politically connected companies, like GE during the financial crisis, benefit from taxpayer-funded rescues, lucrative government contracts, or regulations like GE’s government mandate that consumers purchase its lousy but expensive compact-fluorescent light bulbs.

GE stock rose on the news of the impending departure of Immelt, who is 61, and his replacement with another GE executive, John Flannery, who is 55.

Modest gains may continue if GE keeps working government to its advantage. Flannery heads GE’s health care division, which is heavily government-financed either directly or indirectly.

To really reach Apple, Google, Amazon, or Facebook-level growth, though, GE would have to reach back to the legacy of its co-founder, Thomas Edison, and invent something new or better, like an electric light bulb. Once the invention is made, companies like GE are good for winning political agreements to help get products widely adopted. Without the invention, the firm is just a high-powered lobbying operation. Not that Washington lobbyists don’t make lots of money, but if that’s the route GE really wanted to take, when it recently moved its headquarters out of Connecticut, it should have chosen to head for Washington, not Boston.

Boston, with its colleges and universities and medical schools and hospitals, represented a bet for GE on innovation and ingenuity, not big government. All of Mr. Immelt’s ties to Messrs. Obama and Trump, and the Kennedys ultimately weren’t enough to keep him in his CEO job. Let it be a cautionary lesson for any corporate leader who hopes the route to profits runs through Washington.