How can it be a mistake on their part? They are the ones who proposed the "theory." However, the thing is, I believe you are commiting a non-sequitur. Whereas humans are naturalistic intelligent designers, the Intelligent Designer as outlined in the ID "theory" is by definition non-naturalistic and untestable. If the ID community can find a way to test for a naturalistic Intelligent Designer, then more power to them.
Note: I'm not being sarcastic when I put "theory" in quotes. The thing is, in science, nothing starts off as a theory. You have to form hypotheses explaining a range of related data and if it is confirmed enough and is very accurate, it will graduate to a theory. Nothing starts off as a theory
Because they succumb to the arbitrary, unscientific, philosophical notion that the distinction between natural and supernatural is scientifically valid.
Again, unless science can show intelligent design to be beyond its purview it has no business discarding the evidential products of intelligent design (namely organized matter that performs specific functions) or the theory of intelligent design, as unscientific.
The inequity on the part of evolutionists is glaring. On the one hand they are permitted to construct renditions of history based upon reasonable conjecture and be called scientific, while proponents of ID, when they reasonably conjecture organized matter as a product of intelligent design, are (supposedly) pushed out of the arena. The fact is, there is more physical evidence to support intelligent design than there is to support an intelligent Congress, let alone a billion year history of unobserved, unrecorded processes.