for my aircraft the ground speed difference can be up to 15kt before the IRS is considered unservicable
From a technical point of view I don't see why one would trust a system that allows for a 15 kts tolerance to trigger alerts that require 5 kts or less accuracy. The FDM department should recognize there is a flaw in this logic. If the trigger level is max tire speed +5kts, then in theory an alert could be triggered at 10 kts below max tire speed. On the other extreme, one could exceed the max tire speed by 20 kts before the alert is triggered.
From a safety viewpoint I agree with Cpt_Schmerzfrei; the focus should be on why the plane was operated close to or beyond it's limits.
In your explanation on the calculation of the take off performance you mention altitude, temperature, TAS and IAS. To come to groundspeed, wind plays a role as well. Is wind taken into account in calculating the tire speed? If so, and if the actual head wind component was lower than expected, or a tailwind was encountered, the 5 kt margin given by the performance figures disappears like snow on a hot runway.