Well one easy one, in my country it is that nuclear plants need to emit zero radiation from their core, like nothing. This is incredibly expensive to achieve, a more sensible value would have been similar or less than normal background radiation.
Nuclear has a lot of advantages that are really low hanging fruit of producing safe clean energy that is perfect for a grids baseload.
South Africa, you can read up on us if you want to learn about a country that really fucked up its energy supply, but that is a different story.
You do need a baseload, this is not something an argument of saying we do not really need a baseload can wish away, industries that run 24/7 like a smelting operation where if you cannot shutdown, or hospitals or traffic lights, there is a certain percentage of baseload that has to be generated.
Solar and wind are amazing and I really wish to see these systems play a major role in power generation, but you say the nuclear and coal plants are very inflexible. I do not know who this guy is but Nuclear and coal can very easily ramp up their power generation, both these are basically steam engines, both nuclear and coal can very quickly heat up and generate a lot more steam that powers generators, like an car engine but more accurately a steam train that you give more power to go faster. Solar and wind cannot ramp up on their own, cannot ask the wind to blow harder or the sun to shine brighter suddenly when the system requires it, they need costly backup systems like methane peaker plants or energy storage, be it batteries, pumped hydro, hydrogen electrolysis the list goes on. These things added to solar and wind plants are usually not allocated to the cost of generation, a total cost of generation including these additional backup systems are a better indicator of solar and wind systems cost.
Now what about waste. I agree coal is messy and is causing global warming and needs to be phased out. But nuclear waste is a solved problem, it has been for decades, the spent fuel is usually stored deep underground where it will never interact with the world again. Solar on the other hand, if it costs about $20-$30 to recycle a panel but like $1-$3 to send it to a waste dumps, what do you think will happen to the solar panels. https://hbr.org/2021/06/the-dark-side-of-solar-power Harvard business did an article about how solar recycling has really been a point of weakness, where nuclear we have set guidelines on how to environmentally and safely dispose of nuclear waste currently. I am willing to bet you the environmental impact from pollution from nuclear, including all the disasters will be negligible compared to the waste impact from solar panels and batteries currently.
So my point is not to dismiss solar or wind, really where wind and sunshine are naturally plentiful it will be a waste not to harvest these resources, just like where geothermal resources are available it will be wasteful not to utilise it.
But nuclear, even with its high initial capital cost and long build time, still does provide energy cheaply and will last for a lot longer than solar panels and wind turbines, nuclear can be easily and quickly ramped up or down depending on the load required.