Why would you need long term error correction on an instrument of this nature?
.. because the long term which the aircraft has been flying before you want to use the FPV will have introduced an error in the presentation.
Of course, in the case of V/S, your IVSI may be damped so that that the needle isn't going crazy, but is this necessarily a requirement for the FPV?
Aircraft fitted with IRS don't have IVSI's - because you don't need an Inertial Vertical Speed Indicator when you have an inertial platform (the IRS) already fitted.
(and couldn't it be done electronically anyway, in the IRU?)
It is! This is what I am talking about - an electronic correction to the FPV and VSI presentation, using baro information.