Jean-Marie Schweinberg used a Carrix hiking trailer on his self-contained kick from the arctic circle to Strassburg in 2007. It fastened to a harness on Jean-Marie, not to his Kickbike. It did have two wheels, and while its mounting point was very flexible, there was the possibility that it could tip over, especially with a tall load.
Jim Delzer crossed the U.S. in 2001 on a Kickbike; although he was followed by a sag wagon, he utilized a modified BOB trailer, mainly for advertising it seems, though he could have carried this and that. It has one wheel, better for stability, and a sizeable platform for stuff, but the lower rear-axle mount point of a footbike means that the trailer will ride a lot lower to the ground, though probably no lower than the footbike’s undercarriage.
And then there’s the zen trailer, the one that’s as simple as a footbike, the Extrawheel, which name also effectively describes it. A wheel with a rack attached that fastens with a double fork to a bike’s rear axle. The rack can hold giant panniers, out of the way of a kicker’s feet. It’s stable and light, and available in many configurations, with and without wheels, panniers, etc. Plus, for fun, there’s their photo gallery of some extreme bicycle tourists crossing deserts and the like with them. No reason some kickers couldn’t join them.