here in NZ (no subsidies in our electricity market) we are about 70% renewable via hydro and geothermal. we run a parallel 'reserves' market (everyone does, it's there to take up the slack of a plant tripping out). typically a hydro plant will run 'tail depressed' which means it's not as efficient as it could be but can scale up within 7 seconds (there's another 7 minute reserve market). prices adjust, people get paid to conserve fuel (water) but it's availalbe when needed. fast start gas turbines are also common but these tend to be at the 10-15 min mark (which is still blistering!). tl;dr 'green' energy _systems_ spin up and spin down just like the regular kind...
Hydro is one of the best "green" energy sources, and we definitely need more of it.
The downside is that rivers of the size that can power a Hydro-dam are relatively rare, and ecological issues (flood zones, and whatnot) need to be taken into account.
So I'll amend my original post with Coal, Oil, Nuclear or Hydro.
Solar and Wind are absolutely terrible at "spin up" and "spin down". So other sources are needed to cover the differential.