I do agree that the box fan solution is a great low cost option for small to medium rooms, but if you need 1 device to purify a large area, it's not gonna cut it.
The filter on the box fan also got black faster, which is our indication that it pulled more particles out of the air. Makes a lot of sense, because the actual filter material is the same (they both use HEPA filters inside) but the box fan blows a greater volume of air through a larger filter area.
This is not a good indication.
The larger black particles are not nearly as harmful to you, and generally just fall to the ground. BlueAir and other vertical filters attempt to make sure they don't waste your filter on these large objects, and pull the smaller particles out of the air. Box fans pull a lot off the floor, which isn't super helpful.
The CADR takes into account the differences you speak of, because it measures the amount of clean air. You may enjoy the fans more, but the filter material being the same doesn't mean a box fan cleans air any better.
I realize there are other concerns here (noise, power usage, aesthetics), but at the price points this article is talking about, you can buy 3 box filters for the price of one BlueAir device. Or spend a bit of extra money (but still comparatively less than $400) on a more powerful box fan.
I am doubtful that a BlueAir would outperform a setup with multiple independent fans.
I think it's a feasible estimate of CFM, as the diameter of the box fan's impeller would be larger than the one used in the BlueAir box.