Any reason not to use Tyvek to cover exposed insulation?
Dupont does not recommend Tyvek for interior walls. That said, I've seen DIY sites recommending it over studs to protect insulation as you suggest.

What might be the concerns that Dupont has for interior use? Offhand, I can think of two:


A vapor barrier can cause condensation in walls. However, Tyvek is not a vapor barrier
Fire safety might be a concern.Tyvek is NFPA 285 compliant, but that rating is for exterior walls. Tyvek® FireCurb® is fire-retardant, but still is recommended only for external walls.


Apologies, then... this is really not an answer: Tyvek is being used inside, yet the manufacturer states it should not be.