Playing Devil's Advocate here- an inerter reacts a force proportional to the difference in acceleration of its two ends, whereas a mass reacts a force proportional to its acceleration. The vertical acceleration of the sprung mass of a road car is essentially zero, or not far off, in most driving maneuvers of interest. So an inerter would mainly act like increasing the unsprung mass, which is a bad move according to one of those shibboleths that litter the world of vehicle dynamics.
So why would F1 cars want to increase resistance to wheel acceleration? Perhaps they don't, perhaps they want to reduce the accelerations of the sprung body, for aero.
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