Two wheeled trailers do have their place. I used a one ton two wheeled box trailer for years with no problems, as long as it is built correctly with the axle in the correct place and a decent noseweight, it works fine. I cannot remember any incidents with it in 20 years of use and abuse. Much easier to move around by hand too.
Having said that, I well remember bringing a recently purchased compact tractor with front loader and back hoe attached, back from Devon to Somerset, on a 16' double axle car transporter, and anything over 45mph would start it swinging. I gave in to temptation on one particularly long downhill section of motorway, and nudged 50mph, I was lucky to get away with using just all three lanes, and not the hard shoulder and centre armco as well. That was a lesson learned! Still got the little tractor though.