I generally agree - caveat is for some values of "some simple blur" - the one described in the article is not one in my book.

For reference, for every pixel in the input, we need to average 3x^2 pixels, roughly, where 3 is actually pi and x is the radius.

This blows up quite quickly. Not enough that my $5K MacBook really breaks a sweat with this example. But GPUs are one of the most insidious things a dev can accidentally forget to account for not being so great on other people's devices