What is this "nuclear variability" you speak of? I thought they were pretty constant in their output, unlike wind / solar for which gas plants are needed to compensate.

I think yodelshady is saying exactly that they don't need gas plants to cover nuclear while they do for wind.

I keep hearing they need to be switched off at short notice because… I’m not sure, accidents? I’ve never actually seen a link backing this claim, and I’d be interested.

Nuclear plants need to be switched off for weeks/months at a time for the following reasons:

- refueling (regularly done, highly plannable)

- insufficient cooling water/ too warm cooling water (regular, seasonal, not very predictable short-term)

- planned maintenance (often combined with refueling)

- unplanned maintenance (accidents)

Whenever these things happen, the entire reactor is producing no power. This is why most nuclear facilities have multiple reactors, so you can rotate these tasks among them and still have some power. Unfortunately, the cooling issue is becoming more and more of a problem, and many sites that used to operate year-round now have to scale down significantly in mid-summer due to lack of cooling water.

Why don't coal and gas power plants also have cooling issues?

You can just turn them off. No combustion, no heat. I'm not an expert, but I'm given to understand nuclear reactions don't stop on a dime like that.