Wouldn't it be faster to start from the bottom
I don't remember how the Laine paper reconstructs it, but I do believe the Crassin paper does construct bottom-up. They treat the fragments produced from the graphics pipeline as leafe nodes of an octree, and then build the tree up from these leaf nodes in parallel (I think on the compute shader). Essentially the idea you mentioned.
IMHO, building bottom-up or top-down depends on a few things: 1) you use the right construction that makes sense for your application, 2) the construction method you pick is not overly-complicated for your problem 3) parallelize node construction as much as possible. (important if your on the GPU, perhaps not so much if you're on CPU, and perhaps not important at all if it is done as a preprocessing step and you don't have dynamic objects).
Obviously when using the pipeline, it is faster to construct bottom-up since you have the leaf nodes after the fragment shader (all in parallel), but if you're on a CPU or something, you may just want to construct the tree top-down since that way is generally easier.