1. It's a Bad Idea if there is any chance that anyone will be performing work that requires a hood and is unaware of the shutdown or chooses to ignore the shutdown.  In 2009, a Canadian worker DIED because he performed work with trimethylsilyldiazomomethane during a fume hood shutdown.  I can't find an article that actually confirms the cause of death: https://www.cbc.ca/news/canada/nova-scotia/protective-fume-hoods-turned-off-before-lab-worker-s-death-1.798585   Likewise, workers may not be skilled or informed enough to understand that a shut down hood provides no protection.  At the very least you would have to put huge signs on each hood and tape them shut.  But I still would not underestimate the will of a student intent on finishing their dissertation etc. to bypass these signs nonetheless. 

2. Chemicals or waste stored in the hoods (yes, yes, we all know about proper hood use vs. how they are actually used), may emit vapors, develop a leak, or undergo a spontaneous reaction/explosion that releases toxic or flammable vapors or liquids.  A functioning hood could prevent such releases.

My writeup on fume hoods in the SDS HyperGlossary has various links to fume hood/ventilation considerations: http://www.ilpi.com/msds/ref/fumehood.html 

Rob Toreki