First, a correction. Three Mile Island did indeed experience a core meltdown which the power company suppressed. Don't ask my sources; just look it up yourself.
The biggest problem with nuclear is that all of its problems are unfixable. Cost is out of control, as the OP says. Fukushima, Chernobyl, and Three Mile Island can never be cleaned up. Never. And those are only the household name accidents. The history of nuclear power is littered (literally) with accidents, screw ups, and permanently contaminated sites -- one of which is where the latest PG&E wildfire started. Again, don't ask me how I know this. I spent years doing my homework. But even a cursory review of nuclear power's history will show that it's full of plants gone wrong. Poke around.
The most common unfixable problem of nuclear power is the waste. No one has ever figured out how to deal with plutonium's 200,000 year half life of fatal radiation output. It's a problem at a scale that humans simply cannot address. And don't lecture me about breeder reactors or what they do with waste in France. Do more research and you'll find that I'm correct. There is no working storage or recycling solution anywhere in the world and we're 60 years into the problem.
The OP says it's not so bad because "nobody died," but that's not true either. Again, a little more digging will show that nuclear mining, waste, leaks, and even normal operations affect cancer numbers everywhere they're found.
Who's afraid of nuclear power? The people who sell it. They're afraid the world has figured out their massively subsidized boondoggle and is backing away, which indeed many countries are doing.
A terrific resource if you want more than Facebook-level facts is Helen Caldicott's book, Nuclear Power is Not the Answer. That's a good place to start.
As Einstein said, "It's one hell of a way to boil water!"