Modern reactors can actually ramp up for down pretty quickly, as far a the grid is considered. That is to say, they can go from 50% to 100% in an hour or two.
However, you want to run them mostly constantly because once you build them, they are basically free power.
Besides, Constant power IS what you want for a "stable base load". You can start and stop solar and wind basically at the push of a button for very rapid response.
The point of Nuclear or fossil fuels with respect to the grid is reliability.
No, you can't do that with solar and wind, that's the whole point. Sure, you can choose to waste the renewable energy when it's in excess, but you can't conjure it when it is not.
If you want a grid that has a significant renewable percentage, you don't want stable base load plants, you want power storage, peaker power plants and demand scaling in response to supply.
Cue someone scoffing and saying, yeah, exactly, that's why we don't want any significant amount of renewables on our grid -- Fine! At least that's honest.
The ideal source for base load is something that has an uptime as close to 100% as possible.
Variable load is obviously the tricky part, because that is where you want storage to time shift, overbuilding to deal with seasonal changes, and build redundant peaker plants. This is the really expensive part, far more expensive than building nuclear
The hydro power is not enough as base power for the large cities in the south, on the other hand, in part because in part the capacity is not enough, and in part because how the extremely long transport lines from the far north (where the hydro power is located) to the major cities in the south are a serious bottle-neck. Increasing their capacity (across up to thousands of kilometers) isn't easily done in a few years even.
The thing is though, a lot of heavy industry is built in the North to take advantage of the cheap power there. Shoring up the grid connections would increase the electricity rates in the northern region, due to competition from the South.
EDIT: and yes, if the hydro is far away, it doesn't help much. Besides hydro also depends on weather, although on periods about 10 years or so. But when just once you don't have enough water then what?
In terms of kW/min change rate faster then most gas peaker plants used all over the world.
It is a totally different question if that is economical (the costs of a nuclear plant don't really change much when running at 20% or 100%). So most operators run their plants at maximum if possible just like what wind/solar do when it is windy/sunny. France is the big exception to this due to how large portion of their production is nuclear they have to follow the load with some of the reactors.
But nuclear isn't very good at quickly and continuously ramping up and down. It wants to run at mostly constant output[1]. This makes it a poor companion to renewables.
[1] Except for the couple of weeks a year when it's down for maintenance, refueling, or its river's water has gotten too hot or there isn't enough of it, then the output is zero. Actually, it's negative because you need to provide it with energy or it self-destroys.