When you bring a new turbine online you get it up to speed before connecting it, and you can do this long before it's actually needed. So inertia hurts your response rate slightly but the main factor is how fast you can get your boiler or water pipe ramped up. That's why you see gas turbines as good peaker plants, they have very little to ramp up.
Solar is trickier but it's also more flexible in how it injects power. The real issue is not lack of inertia but the fact that it can lose production when a cloud comes by.
Reading around, as the amount of renewables (solar) increases this might become an issue due to less turbines being in use.
"spinning up a turbine"
As in spinning up to speed. It can't go 0 to X000 rpm instantaneously. Inertia!
Didn't realise they were designed to spin at a constant speed though, thanks.