One problem with nuclear power is that it's often used in areas that are unsuitable for it. Most of the world doesn't have to deal with earthquakes and tsunamis quite as often as Japan does. Most countries would accept foreign aid after a disaster, unlike Japan and the USSR did after their disasters to save face.
People also stopped developing reactors when Chernobyl happened. Of course, the Chernobyl reactor was already an outdated reactor by the time it failed, but the problem is clearly visible in reactors that have been maintained and kept for prolonged lifetimes bexause of necessity (for medical supplies, for example).
I can imagine a future where renewable energy can serve most of the world's power demand, with nuclear reactors kept as a backup in case of prolonged bad weather draining the batteries/energy stores that keep the excess solar/wind energy.
People also several understate the damage traditional coal plants cause to their direct environment, which funnily enough includes excessive radioactive materials.
Switching away from nuclear because of Chernobyl, Three Mile Island, and Fukushima feels similar to banning planes or skyscrapers after 9/11. Disasters happen and leave incredible death tolls, but they're not common in the slightest.
I'd reckon you're far more likely to get sick because of a coal plant leaking coal ash into the air you breathe or the water supply than being nearby enough to a meltdown to be affected.
Gas and oil plants suffer far fewer downsides, but they still incur a cost on the environment that some countries have decided to ignore. They use more fuel but require less cleanup if you don't consider complete carbon capture as a necessary cleanup step.
Some areas can't get nuclear power. I'd consider the entirety of Japan to be a terrible fit for such power plants because most of the country is either in a disaster zone (tsunamis or earthquakes) or has no access to cooling water. With little access to fossil fuel sources and a highly dense population Japan hasn't exactly had many alternatives for many years, so I understand why they went nuclear anyway, but I wouldn't build a new nuclear plant there now that wind and solar are cheap enough that the supplies need to be maintained artificially in some cases.
Areas like Tornado Alley and cities built on top of super vulcanos are also an obviously terrible fit for nuclear power, as are countries plagued by terrorism and corruption, and countries bordering hostile powers with no remorse for the population like Russia and China. However, in a safe country with a decent grid, you can build more safe nuclear reactors than you'll ever need in the places that do qualify.
Nuclear can work and it can work a whole lot better than fossil fuels can, but it's not a magical solution that you can just put down anywhere for cheap power like some advocates seem to claim it does. I believe the current anti-nuclear sentiment is largely fueled by unnecessary fear and the freeze on research and construction will have a self-fulfilling prophecy effect as old reactors won't be replaced with newer, more efficient ones, larger and larger percentages of nuclear reactors will be shut down and cost more and more as nobody is willing to invest in them, and more and more unmaintaind reactors will likely suffer accidents.