If the tandem trailer is still functional on one axle, then that axle is sized for the entire trailer weight, and the extra axle is adding zero capacity. On the other hand, if you try to size so that each axle (with its set of wheels and tires) is so light that it can only handle half the trailer weight, then one axle will always be overloaded, because they never share load quite evenly.
I can believe that a minimal axle with 12" wheels and tires (and no brakes) is only about 80 lb... but that's a meaningful fraction of the weight of a small trailer. At the size of a Compact, it's an inadequate axle - each of the tandem axle assemblies would likely be heavier than 80 lb.
Tandems are interesting, but a tandem setup at a weight that a reasonable single axle could easily handle (such as the Compact) doesn't make sense to me.
Small tandem fans might like the Fiber Stream. I think it's too large to be considered a "tiny" travel trailer, but it's hard to find a smaller tandem.