Any single wheeled trailer will put some stress on the rear wheel, mostly due to sideways torsional stresses from rocking from side to side while standing. But also some stress from the "tongue weight" as well. It's best to have a robust rear wheel when towing a single wheeled trailer.

Most two wheeled trailers are designed to have the load centered over the axle of the trailer and are more stabilized. I've seen people tow two wheeled trailers with racing wheels with no problems.

There are pros and cons either way.