The libs always thought Reagan won by doing something similar. It was a lie, of course, but as much as they like projecting I can easily believe the gist of your theory.
Except they forget Reagan wasn’t running as the incumbent.
Campaigning with one or more members of the Diplomatic Corps being held hostage by third-world barbarians, then securing their release by releasing another murderous barbarian is NOT a sure-fire recipe for electoral success.
Reagan won by projecting Reagan. The American people knew he would protect us and the muzzies knew they would have to deal with him and not the befuddled Carter.
Reagan had Carter looking weak and stupid because our embassy was being held hostage. Carter won no points by having hostages taken then doing nothing....appeasement in giving up the blind creepy terrorist would have gone over worse than sitting around and taking it!