The Cold War didn't pretty much end because of Reagan, it just pretty much ended while Reagan was president. The Pope probably had more to do with that than Reagan did. Teflon.
"At the start of the Iran-Contra investigation, Attorney General Edwin Meese had set the time parameters from 1984 to 1986, thus keeping outside of the frame the possibility of a much more serious scandal originating during Campaign 1980, i.e., whether Reagan’s campaign undermined President Jimmy Carter’s negotiations to free 52 American hostages in Iran and then paid off the Iranians by allowing Israel to ship weapons to Iran for the Iran-Iraq War.
So, while congressional and federal investigators looked only at how the specific 1985-86 arms sales to Iran got started, there was no timely attention paid to evidence that the Reagan administration had quietly approved Israeli arms sales to Iran in 1981 and that those contacts went back to the days before Election 1980 when the hostage crisis destroyed Carter’s reelection hopes and ensured Reagan’s victory.
The 52 hostages were not released until Reagan was sworn in on Jan. 20, 1981.
Over the years, about two dozen sources – including Iranian officials, Israeli insiders, European intelligence operatives, Republican activists and even Palestinian leader Yasser Arafat – have provided information about alleged contacts with Iran by the Reagan campaign." https://consortiumnews.com/2013/03/09/rethinking-watergateiran-contra/
If he managed to restore faith in American politics, he was only able to do so because he discredited his predecessors and cover up his own involvement in his clandestine operations more discreetly than they were.