Reagan scared the crap out of a lot of the rest of the world.
Which only a fool thinks is a good thing. But there are a lot of fools who fantasize about other people being submissive toward them because they're scared. The problem is that scared people don't necessarily act submissively. They often respond aggressively as well.
Put in a Cold War context, the Soviets and the US were in a Mexican standoff, with both sides having their hammers cocked and fingers on the nuclear trigger. In that situation you don't want to alarm anyone, but that is exactly what the senile fool did.
That summed up the election right there, Americans didn't want another 4 more years of someone who could be attacked by a rabbit.
I voted in that election, and I remember it well. You capture the way people were thinking accurately, but not critically. Anyone can be attacked by a (possibly rabid) animal; it wasn't a real issue. There were three actual substantive things people were reacting to in the election: (1) stagflation, (2) the Iran hostage crisis, (3) the energy crisis. While Carter's leadership style might leave a lot to be desired, it's hard to criticize his actions in any of these situations.
(1) Stagflation was the result of his and Paul Volker's successful attempt to ward off imminent hyperinflation by a combination of austerity (reducing the federal debt-to-gdp ratio of 3.3%) and sky high Federal Funds rates. Economic growth resumed pretty much in sync with the reductions in Fed interest rates, in fact under the last Carter budget (Presidents in their first year govern under their predecessor's last budget). Arguably milder steps might have done the job without causing the recession, but the fact that inflation continued even as the Federal Funds rate hit 20% suggest that weaker measures wouldn't have worked.
(2) Carter's handling of the Iran crisis is probably what brought his presidency down, but it came down to this: the military was still dealing with the aftermath of the Vietnam war and couldn't execute the rescue mission successfully. Contrary to popular myth Carter actually raised military spending, from 282 billion under the last Ford budget to 303 billion under the last Carter budget. Yes, some big programs were eliminated or trimmed, but ironically operations and maintenance was a major area of increased spending in Carter's budgets.
(3) The second oil crisis was caused by the Iran Iraq War. In response Carter deregulated oil prices, which caused domestic production to rise and imports to fall.
In short, Carter was the kind of president people think they want: honest, prudent, and responsible willing to do unpopular things because they were right. Had two of the eight helicopters in Operation Eagle Claw failed instead of three, he'd be remembered very differently.