In the USA we do things a bit differently; what a surprise. Trailer hitches are generally two piece: a receiver (sturdily mounted to a structural member on the car) which RECEIVES the ball unit. Two of my cars have built-in from the factory receivers, but the ball assembly is the responsibility of the owner. The receivers are classified by weight, in Class 1-Class 5. My two Ford SUV's (Edge and Flex) both have Class II receivers, though they carry different tow limits. Class 1 is a very small capacity, for smaller cars. Class III would be on a lighter duty pickup truck, and the more robust the pickup is, will determine if class 4 or 5. A RAM3500 or GMC3500 may qualify for a Class 4 or 5. The receivers are generally 1" square for Class 1, and 2" square for higher.
I mention this since it seems to be vastly different than what I used to see in Europe, though it's been some years. The photos presented here of the Pagoda hitch assembly matches my memory: an integral ball on the end of a round bar that simply disappears under the car. No visible receiver, no interchangeable ball. I did used to see very lightweight "caravans" towed by the thousands from Northern Europe to Southern Europe for the summer holidays.
While it may be nostalgic to keep this on your car for an homage to the past, your legs will thank you if you leave it off.