Actually, many states do require brakes on anything that is towed, often based on weight. Typically, towed trailers or cars over 3000 lbs require brakes, but some states have exceptions specifically for cars under tow. It can be pretty complex to determine exactly what applies in each state. Further, the motorhome chassis manufacturer sometimes stipulates a max weight the chassis can tow without auxiliary brakes, typically 1500 lbs. They will also note that the motorhome brakes are rated only to stop the coach GVWR, not the full combined weight of coach and towed car or trailer.
Last, there are the laws of physics that apply to objects in motion. Auxiliary braking always stops the rig in a shorter distance. That may not be important until somebody in front stops suddenly or pulls out in front of you. Then every inch counts!
Most states do not require separate lights on the towed car if the dolly has lights that are visible, but that's a judgement call where the law enforcement officers opinion has far more weight than yours.