Maybe the reinvention could get automated? Like, any agency is going to be shut down and rebuilt without previous staff every 30 (or whatever) years after it was originally formed? Hard to see how the transitions from old to new version would be done unless you kept outwardly backwards compatibility, though. At least it could shake things up internally.
Norway is actually doing this a rebuild of one agency. The Government's Road Agency has essentially been deigned ineffectual and FUBAR, so a new agency has been formed (New Roads) with responsibility for all new roads. The old agency has stopped replacing retirees (I think) and will eventually disappear. This is of course never said loudly in plain words. I just wish they would do the same for the railroads agency, which is a peerless shitshow.