I used a KarKaddy II for over 25 years without a problem, towing a variety of cars, large and small. The Kaddy does not have a suspension since the vehicle being transported uses it's suspension for stability. I would hook the safety chains over the frame when the car did not have tow rings. But the safety chains are loose, meant for a break-away situation, not as a tie-down. The tire tie-downs are tight, allowing the car to bounce freely during travel. Not that I question your mechanic, especial if he is a friend but; I have been told that dirt on the shocks means I need new shocks, I need brakes since I only have 20% left, and corrosion on the battery cable is a sign I need a new battery. Some of these guys work on commission. Get a second opinion.
As for the back getting the full affect of the bumps....guess you better not drive the streets of Los Angeles, Some of the potholes are so big you could park a Smart Car in them.