> "How did the 'engage economically to change the regime' policy work with China and Russia?"

China and Russia didn't engage economically to change the regime. They did it to make money.

> "For that matter, did Cuba change at all after Obama's attempt?"

YES! When Obama engaged Cuba, the entire political calculus of the country changed almost overnight.

"As Obama began softening U.S. policy toward Cuba, the island signaled openness to reform under the new leadership of Fidel’s brother, Raul. Facing an aging population, a heavy foreign debt load, and economic hardship amid the global downturn, Raul Castro began liberalizing Cuba’s state-controlled economy in 2009. Reforms included decentralizing the agricultural sector, relaxing restrictions on small businesses, opening up real estate markets, allowing Cubans to travel abroad more freely, and expanding access to consumer goods. Cuba’s private sector swelled as a result, and the number of self-employed workers nearly tripled between 2009 and 2013.

Obama and Raul Castro surprised the world in late 2014 by announcing that their governments would restore full diplomatic ties and begin to ease more than fifty years of bilateral tensions. The historic moment marked the culmination of eighteen months of secret diplomacy brokered by Pope Francis in which the parties agreed to an exchange of prisoners, including Cuban intelligence officers and an American development contractor, among other concessions."

U.S. policy towards Cuba was turned 180 degrees in 2016 in a unilateral move by the U.S., so that ended any hopes of progress.

"As a candidate, Trump was fiercely critical of the Obama administration’s thaw with Cuba and he pledged to reverse course once in office. Despite maintaining diplomatic relations, Trump has largely delivered on his promise through policies that curtail trade and tourism, and target Havana’s purse strings."

https://www.cfr.org/backgrounder/us-cuba-relations

> "Engagement fails when it is not reciprocal"

Iran was very open to cooperation with the United States following 9/11, right up until they were included in the 'Axis of Evil.'

"In the aftermath of the attacks, the Iranian public responded with sympathy and their government with something resembling prudence. Tehran was the scene of spontaneous candlelight vigils by ordinary Iranians and a temporary suspension of the weekly chants of “death to
America” by its official clergy. An array of Iranian officials, many with reformist political leanings, offered seemingly heartfelt condolences to the American people, and even the hardest-line elements of Iran’s leadership briefly summoned the moral decency to denounce Al Qaeda and the use of terrorism against Americans."

...

"The initial willingness to cooperate with the U.S. military campaign against the Taliban eventually bloomed into a wide-ranging, historic cooperation between the two old adversaries that included the only sustained, officially sanctioned dialogue since the negotiations of the hostage release in 1981. Logistical cooperation from Tehran facilitated use of Iranian airspace as well as tactical assistance in establishing supply lines. Equally vital was Tehran’s political collaboration, as the Iranians had close and long-standing relations with the Taliban’s primary domestic opponent, the Northern Alliance."

...

"The “Axis of Evil” speech produced a furious response from Iranian leaders across the political spectrum, and incited a similarly fierce debate in Washington. It did not, however, result in the termination of the bilateral dialogue over Afghanistan, as Tehran demonstrated its capacity to prioritize interests over outrage or ideology. But it marked an across-the board American repudiation of Iran’s ruling elites, one that would become more pronounced over the course of the subsequent year, and a deliberate U.S. embrace of the idea of galvanizing popular opposition against the Iranian regime. In the months that followed the speech, the Bush White House strove to align themselves with regime opponents through public statements and other efforts to expedite political change inside the country."

https://www.brookings.edu/wp-content/uploads/2016/06/11_iran...

(It's from a Brookings whitepaper, but it jives with the gist of The Twilight War by David Crist)

The U.S. keeps turning its back on both countries when progress begins to be made, based on old animosities left over from the Cold War. It's ridiculous. Why does the wealthiest country on the planet need to be in a pissing contest with a small Caribbean island nation over something that happened under the Kennedy administration? Or a theocracy on the other side of the planet over something that happened under Jimmy Carter? My god, what's the point?