No problem at all. Look at the handlebars of the bike–they are designed to handle the crushing load of a stem clamp and take it like a champ. The top tube of your bike isn’t specifically designed to resist crushing, but it is designed to handle combined loading (shear+bending moment+axial loads) quite well, and the pressure applied by a rubber strap will not be anything close to what is required to damage your bike. That said, you may want to put a rag or two on your top tube if abrasion is an issue with your car. My truck is wide enough that the bike is entirely blocked from the freestream highway air and thus does not swing, but if your bike tends to swing back and forth then I would recommend wrapping the top tube in an old T-shirt, padding any potential contact points on the rack, and even strapping the bike to the rack itself. Also, make sure your handlebars can’t swing around and impact your top tube. This can and will damage your frame. Over the last 3 years and several thousand miles, a small ding to my top tube from the handlebars (vision tech base bar) is the only damage my bike has incurred due to carrying it on the hitch rack. During the same period of time I had a Yakima roof rack fail on me, and my bike was dropped on the roof of my car at 65mph in a construction zone on the way down to Florida. My dad once forgot to replace the pin in the pivoting part of the rack and the hitch rack pivoted down with my bike on it at about 20mph but everything was fine in both cases.
Side note: I wouldn’t consider the hitch rack superior or inferior to the roof rack. The safest place for your bike is in your car, but both the roof rack and the hitch rack have risks involved. Roof racks are susceptible to low overhanging things like tree branches, parking garages, drive thru’s, and the side of your house if you forget the bike is on the roof and try to drive into the garage. They’re also at an increased risk for damage due to debris that flies up from the road. Getting a bra for your bike will help, but may not protect against damage due to more massive objects. Granted, it’s not every day stuff like that flies up from the road, but I’m just saying…the hitch rack, on the other hand, protects your bike from debris flying off the road, as well as a larger percentage of rain/hail/bugs or whatever. It is also at an increased risk of getting damaged in a rear-end collision. Either way I can’t say for certain which is more secure (secure being defined by the factor of safety (ratio of normal operating load to load required to un-seat your bike from the rack)), but as long as you use the rack correctly it should safely carry your bike for many miles.