U-Haul tow dolly for FWD cars have straps for the tires and a chain as well; certainly other vendors are similar.
Obviously the car's suspension does the work in this case.
Downside of this method is the vehicle needs to be able to safely roll on the highway; and, can that be guaranteed after a race?
Based on the other loads I've towed, I think it depends on the load and the trailer (or truck). YMMV.
If I have a dead load - un-sprung - I strap or chain it to the trailer, and clearly the trailer's suspension will have to do all the work of smoothing out the trip. I've never had a problem strapping down a dead load.
With a sprung load on a trailer, I experienced losing a strap before I even got off the property where I was collecting the load. There were a lot of ruts and potholes in the collection area, and I didn't even get out of the restricted access area before the strap came loose.
I was collecting a light sprung trailer not suitable for the highway, and had strapped down the purchased trailer onto my heavy collection trailer, by twice going over the purchased trailer with straps, with a chain on the axle. There was enough give in the springs that I lost the hook on one of the straps from the pocket I hooked it on.
As soon as I got past the gate, I immediately pulled out of the aisle and parked, and I changed how it was secured: two chains, two load binders, and another strap [it was an odd shape light trailer] secured by shrinkwrap holding the hooking method secure for the strap.
Straps stretch slightly, and I love shrinkwrap for holding hooks secure onto hooking points. I was running out of time to get out of the restricted access area, so I skipped the shrinkwrap at first until I passed the gate.
Later, I collected a heavy vehicle [GMC Savanna mini-schoolbus] onto that same heavy trailer, and I just used chains and load binders on axle members.
Yes, there was some action of the vehicle on the trailer, separate from the trailer itself. That, plus the weight balance and the airflow, seemed to cause the fishtailing of the trailer over about 60mph in a straight line (I found that out within 7mi. from the pickup point). So I kept it under that, and had no problems - except for the 18-wheelers and the buffeting when they blew by.