I have a couple stories here to persuade you one way or the other.
My buddy Rick has a roof mount rack and routinely put his road bike on top of the car to do group rides after work. On the way to work, he whipped into the parking garage and forgot the bike was up there, and the bike smashed into the garage and shot off the car like it came out of a cannon. There is a sweet dent in the head tube from that one.
Another day he came home from a ride and backed into his garage, once again, forgetting his bike was up there, and watched the bike ride down the windshield and into the street.
He decided at that point to get a hitch mounted rack to prevent that from happening again. I hooked him up with a girl I knew who raced, and they went to a race together, with their bikes on the back rack. Of course he put hers on last.
They got to their destination, and realized her bike wasn't there. It fell off somewhere in the last 100 miles.
They called the highway patrol as a last resort, and surprisingly they had it. They picked it up all mangled and shit.
Moral of the story: Get an SUV.