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If you're going to put children in it 2 wheels is practically essential, you need to push it about with the kid(s) in it either hitched or unhitched and it has to stand up.
We've got a Thule, which is for transporting 1 child and it has little clip in/out front wheels for pushing it about when unhitched and for multifunctional use as a rather cumbersome push chair. It's got basic suspension (leaf springs), which you might not need for cargo transport. It's got no brakes, which I find a bit odd, but they're obviously a big challenge for outboard wheels and keeping the trailer easily attachable to different bikes. Nonetheless, relying on ordinary rim brakes going down a reasonable hill with trailer+firstborn on the back seems a bit dodgy - I'd quite like a drag brake on the trailer, maybe on/off controlled by a friction shifter (discussed in one of the tandem threads?).
There's a discussion in the cargo bike thread I think about putting a car seat in the cargo bike using an isofix attachment. Something like that would look like the most promising way to have multifunctional child and cargo transport. But unless for nice weather fun only, you'd still have to attach a pretty important superstructure for weather protection, and I think it is also meant to serve as a roll cage for the type of crash that doesn't bear thinking about.
Recent designs of child carrying trailers are so functional that there seems little fun about them - I guess the designs have converged on two wheels, forward-facing children, strapped in a cabin, with backups on all the joins in the hitching mechanism, because that seems the best way to make them safe and practical.
As a non-parent, what I would really like is something that offers flexibility.
In order to achieve that I think that realistically I would be looking for something with a simple, two wheel base and then an expanding range of modularity that could be built on that. That could be from a simple flat base to a child carrier or a mobile trading stand or something more complex.