grid-scale batteries generally do add inertia, because that's the most valuable service for them to provide at a small scale. Inverters attached to batteries can do it way better than spinning generators, but they need to be set up to do that.

(And a DC grid would be much more difficult to manage: the nice thing about frequency is that it has to be pretty much the same over the whole grid, so it's a useful signal for the balance between supply and demand, while voltage is really quite sensitive to local effects)