If the inertia of turbines helps cover small loads, couldn't that be scaled up with a bunch of flywheels connected to motor/generators? Seems like it would be better able to handle sudden changes in the network than batteries+inverters.
Yes - this is precisely what was trialled in the UK a few years ago. You can basically take old decommissioned generators and just take power to spin them up - thus, you've just (re)created rotational inertia on your grid. It's a bit absurd, but it does work!