Let's consider slightly older vehicles. Or, for that matter, even newer ones. How many parts on a car could be profitably swapped out with low value replacements while allowing the vehicle to remain operable? One could certainly replace a water pump with an older one, but it couldn't be so badly damaged that the vehicle could not be driven a few miles. What's the marginal difference in the value of the stolen part vs. the semi-operable one? Is the sum total of these marginal differences minus the cost of renting the vehicle sufficient to make this crime worthwhile? For non-commodity vehicles (a Honda Civic w/ many aftermarket parts, etc.), I can see positive ROI for the thief, but owners of such vehicles would no sooner rent them out than they would offer up their pets or girlfriends by the hour.
For the individual owner without fleet economics to back them up, however, one individual event (ie, theft, major damage) can be enough to put them out of the pool.