It's been 40 years since I worked for Duke Power (now Duke Energy) in the production department. I had involvement in coal, oil, gas, and nuclear; we had hydro, but it was a different department.
I think your understanding of the ability to change output is over optimistic.
Nuclear, UNDER NORMAL conditions, can probably change less than 10% per hour; I'd guess more likely 5%. It also cannot (I'm guessing here) operate well at less than about 60% of nominal. From a cold reactor to 100% generation is more than a day, less than a week.
Coal is better. If designed to do so, (and when I left in 1978, none of ours were), steam turbine operation at 40% was about as far down as it could go; ours were practically limited to 65% or so. Cold startup is worse than nuclear because temperatures are higher ... maybe 650F for nuclear, 1050F for modern coal/gas/oil. But they can probably go from minimum to maximum, or the reverse, in about an hour without undue stress. A gas fired boiler won't differ much.
For reasonable efficiency, a gas turbine will be part of a combined cycle system, with waste heat boiling water for a steam turbine. The lower temperatures allow cold startup of the boiler in probably an hour; the gas turbine can probably be at full load in 20 minutes. Neither of these will operate WELL below 50%.
Hydro is the great one ... 0-100% in a minute or two. But IIRC, we got maybe 4% of our needs from hydro.
I don't think anything except hydro can handle the minute-to-minute variation of renewables. By allowing slight voltage and frequency variation, and with the small amounts presently talked about, fossil can do pretty well. But if solar approaches 20% of the system, even handling the 10AM to 5PM smoothly varying output won't be easy. A cloudy day, from the utility standpoint, is much easier.
As our Brit said, we've got to come up with some effective storage, probably (my guess) in the 10% of daily energy load, to handle 25% or more renewable generation.
I don't think batteries are YET worth considering, but AFAIK there isn't anything except them and pumped storage. Of course, perhaps the load can be leveled; businesses, schools, industries operating more hours of the day, especially in summer when the nights are relatively cool.
It's interesting that Duke's pumped storage systems were originally intended to allow the nuclear units to operate at substantially base load.
This is just my view, and I hope some CURRENT experts can shoot my pessimism (realism?) down.