It's useful in traditional grids because we didn't have electronics that could more or less instantaneously respond to load changes - they had to rely on spinning generators instead.
But, this is a precipitous arrangement. If there is any drift in the clocks or some fault in the sync protocol, you can quickly wind up with a completely dead grid (because all your inverters will have killed each other).
Spinning metal is very simple and robust. The failure modes are all much more gradual in nature. Today, one or 2 bad inverters would not start a chain of horrible events because hundreds of tons of metal are not easily perturbed. Without inertia, a bad element in the grid can have substantially more impact.
A grid without rotating generators would act differently, for sure, as you won't have varying frequency to indicate if the grid is overloaded - you'd have to rely on different measures to understand how close parts of it might be to failure.
"Bad actors" in the grid can already cause severe problems regardless of spinning generators; if a power station goes offline the unexpected load spike can easily trip off most of the grid anyway. Smaller, distributed generators/inverters if anything are more reliable, as a fault in one is less likely to constitute an outsize portion of power generation. "Grid inertia" today is largely a result of the total machinery attached to the grid just massively outweighing any individual actor.
The rotating machines are wholly as dependent on controls as the inverters.
Besides "synthetic inertia" on the PV inverters, there exist also synchronous condensers (basically a motor/generator spinning a heavy mass) which can already be found in many substations.
Wait what, Newton's inertia was about physical objects, not voltage stability? You talking base vs peak demand or what?
On the surface this is very true. However, types of solar have caveats that do not manifest until you have a certain amount of utilization in the grid. Photovoltaics do not contribute to inertia. This is the Newtonian concept that ensures instantaneous voltage stability separate from any active demand/generation management functions. The more inertia you have, the more work it takes to speed up or slow down the grid.
Hypothetically, a grid that is 50% PV solar and 50% others would experience severe stability issues if the other class of generation were to be substantially impacted (i.e. your big-bang-for-buck military targets).
You cannot run a power grid on PV solar alone. It just won't work at scale.