I agree on them being safe - when rules are properly adhered to, they're extremely safe, similarly to air travel. People only suspect their safety because when they do fail, they tend to fail spectacularly, again similar to air travel.
Having said that, they may be efficient to operate, but they are by no means efficient to build. They cost a lot of resources, and have a 10 year lead time - plus you need to worry about the cost of waste storage and decommissioning.
So sure, nuclear is better than fossil fuels, but you're just kicking the nonrenewable can down the road.
That time and resources would be far better spent on renewables, because that where humanity is gonna have to go long-term no matter how well any other alternatives work.
Isn't the whole thing with renewables that we can't ramp production with demand and don't have storage figured out? Use renewables as much as you can, and use nuclear to fill in those gaps.
The storage will probably have a similar lead time anyways and isn't as proven as nuclear.
Nuclear is the worst possible option to fill said gaps. Nuclear reactor need to run at a mostly stable output permanently, they are slow to react to changes and can't be switched on or off at will.
You could use them to generate a stable base power level, but that's the opposite of what we need. It wouldn't change anything regarding the need of energy storage.
The best option currently as a gap filler is gas cause it can be turned on or off in minutes when needed.
Not keeping up with demand is a self-made problem. Multiple EU countries already have multiple days a year where they use 100% renewables.