Plenty of "libertarian" Republicans were behind Reagan, but was the Libertarian Party? Murray Rothbard certainly wasn't. At least some libertarians were ferociously anti-Cold War.
One thing about bringing together the conservative movement -- plenty of Republican and conservative voters aren't "movement" people, and too many "movement" noises may scare away the Republicans' pluralities.
One advantage they had that we don't have is that they did it at a time of occupation of the government by the Far Left.
Easier to rally people to oppose horrid liberalism than to organize coalitions for a positive and pro-active push for conservatism when the Left isn't oppressing everyone with their control of government power.