A totalitarian system cannot be defeated by economic means. To periphrase Bill Clinton, "Economy doesn't matter, stupid". (Look at North Korea). What Reagan (and Thatcher, and John Paul II) did - each in their own way - was to present the Kremlin with a challenge the Kremlin was not ready for. The Soviet elites panicked, started "reforming" the un-reformable idiotic (economically speaking, from the Western point of view) structure, and everything quickly fell apart, and the rest is history.
Does Ronald Reagan deserve credit? Absolutely. As the Russian joke goes, if Carter were re-elected, Brezhnev would be still alive. But all he and his cohort really did was to insist on the superiority of the Western liberal constitutional democracy, as compared to the most hideous political pathology in the whole history of human race.
There are, after all, some elementary truths, "absolutes". Apparently, it takes a huge hero - or at least a "charismatic leader" - to make us remember that.