This is largely a myth. Plenty of trailers do have shocks. However, the primary benefit of shocks, which is a smoother ride, is not a high priority for small trailers like campers and utility trailers. Most modern commercial trailers do have shocks. The shocks offer smoother ride which is essential when transporting fragile and live products.
Going back to smaller trailers, the addition of shocks add weight which increases the burden on the towing vehicle. One could argue that having shocks can pay dividends despite the additional weight. The dampening action helps minimize bouncing to keep tires on the road when the trailer is unloaded. This makes the trailer easier to manage. The reduced vibration lengthens the life of the parts of the trailer.
However, just because trailers don’t have shocks does not mean there is no dampening. Instead of using shocks, manufacturers have reassigned the task of dampening to the tires. The sidewalls of trailer tires have different construction when compared to light vehicles.
The trailer tires are designed to flex more to absorb the vibrations generated by the springs, thereby acting as dampeners. Although they don’t perform as well as shocks do, the reduction in vibration is quite significant. Trailers are never going to be comfortable for people, but that is really not important. The only time a trailer can have a passenger is when that person is keeping important secrets and being tortured for it.