There are many classical physics experiments you could do where you understand all the physics and formulas to excruciating detail and you control every variable but you still can't get the same results everytime. Things like throwing dice, as mentioned in the article, or the chaos generated by flowing fluids. Given that any superdeterministic mechanisms would be even even more complex and weird and unknown it seems impossible to disprove. Any failed experiment could be excused by saying that there are more unknown uncontroled variables.

Well, the determinist would argue, that, if you cannot predict the result reliably every time, you do not actually know all the variables, even if you think you do.

Setting up such an experiment means to control hidden variables, but then they aren't hidden.

That's the whole point right? The hope is to figure out what the hidden variables were, to make better predictions than quantum mechanics could. To un-hide them, as it were.