- they only work with 2 variables, but many interesting problems require digging into more variables
- they only work with medium-sized numbers, and aren't readable when P<0.01 or P>0.99
So they're great for gaining intuition (like the Simpson's Paradox example), but when you try to solve a real problem you find yourself boxed in.
In most real situations, they wouldn't be very practical. As you note, the core trick in this essay only works for 2 or 3 variables, assumes they're discrete, and doesn't scale to the variables having lots of values or really improbable values.
There are visualization techniques which are useful in the real world, at least some of the time -- a lot of my blog explores this in the context of neural networks -- but that wasn't my goal in this article.