Wouldn't it be easier to do with the downspout vertical, and once the roots approach the base, plug it into the pond basket? As is, I would expect the roots will grow downwards to the bottom of the tube
Sure, the roots are probably going to grow downwards to the bottom of the tube initially because of geotropism. However, there's only a small volume of nice akadama, pumice, and lava to grow into there. The tree is going to quickly run out of places to grow roots in that hospitable zone. After that, the only place to go is up, through the pea gravel, until it gets to the top of the tube, and then down again until the roots reach the pond basket. I could've just placed downspouts vertically in pond baskets, and indeed I have done exactly that for several other plantings, but I did this one differently as an experiment. I don't expect that geotropism will actually be a significant impediment. My expectation is that the entirety of the tube and the pond basket will be fully populated with roots within a couple of years. Thirsty tree's roots are going to go wherever there's a balance of water and air.
Why go to the trouble of making this apparatus? I'm planning to let it grow for quite a long time without repotting. Typically, when folks do exposed-root style plantings, they start uncovering the roots fairly early on in the process in order to wire the roots into a desired shape while they are still young, thin, and pliable. So, you could plant a tree in a vertical downspout and start uncovering the roots within the first year or two if you want to wire them into shape for a cascade. The downside is that thickening of the roots is slowed down some by the uncovering, wiring, and repotting. With my experimental setup, the plan is to only uncover the very end of the tube early on just to wire that portion of roots into a nice conical shape, so I don't end up with a tiny trunk that transitions suddenly into a wide tube shape. But, I don't intend to uncover more than just the very end part of the roots to wire them and wrap them back up with a bit of sphagnum moss. The remainder of the roots are going to stay in the tube, undisturbed. The roots themselves should hold the substrate in place fairly well against erosion.
That's the plan anyway. We'll see in time what nature actually chooses to do...