Aren't batteries quite limited in their ability to provide synthetic inertia? Sure, they can respond on a second or tenth-of-second scale, but they don't provide the kind of instantaneous inertia you get from spinning rust. Inverters aren't exactly designed to just eat power surges, they'll instantly disconnect instead.

That's why the UK grid has been building some "high-inertia synchronous compensators", and a 2019 outage showed that it's urgently needed.