Extract from the quote in Giblet's post (last paragraph):
Other innovative tuning elements featured on the FW31 include front and
rear devices called inerters. These inerters literally add inertial mass to the
un-sprung suspension without actually adding weight to the wheels, thereby
avoiding the pitfalls associated with extra weight. More inertia will reduce
the ride frequency or response time of the suspension just like a heavier
wheel would, and may be beneficial over different types of track surfaces.
In some instances a lot of inerter mass will be beneficial and at other times
no inertial mass will.
With respect, I don't think the paragraph is quite correct. In the configuration used in F1, inerters & increased unsprung mass have an effect that is similar for some vehicle response properties, but the effect on others is quite different. Overall, used sensibly, inerters can help the aero/mechanical set-up compromise. Whilst they may not always deliver an improvement in single lap performance, I can't imagine a situation where inerters would have an adverse effect on the performance of a vehicle with good structural integrity.