I probably would if I didn't already have a car that was paid for years ago.  Renting a car three times a month costs more than the parking garage.
Why don't you join a car sharing program?  I've never done it but the idea of having a car sit in your parking spot for days on end just depreciating would drive me crazy.  
 
Would it be better if you kept it company while depreciating?
They do more than just depreciate, they rust pretty bad if you don't drive them as I found out when my disk brakes needed to be replaced after 3 years and 5K miles.  
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