I know people do this and have never heard first hand of anyone having a problem.
A friend used to travel from Coquitlam with foamies directly on her roof. Even with a good bow and stern line, the kayak would end up a diagonal on her roof. I did not like to drive behind her! When she bought a new car she made sure she had a decent rack.
You will get a drip into your car..
Most importantly, no one will rent you a kayak unless you have a roof rack, by which I deduce they identify it as a hazard on the road. Insurance is qualified by the load your rack is rated to carry.