Some people searched for structure of the atom, and found great things. Other searched for perpetuum mobile, and found nothing. We know that they will never find anything, but it does not stop them, there are still youtube videos being made today.
It's important to tell former from latter. Unexplored things are not the same as things that have been explored and found false.
People started searching for the structure of the atom in like 400 BC and didn't make any progress until they knew how. We know why perpetual motion isn't going to be found, so there's no reason to look for it in the first place. This isn't a relevant argument.
Searching for animal intelligence certainly feels like an exhaustive search of all possible perpetual motion machines, and similarly, people keep on enthusiastically nearly finding it. And of course this is plagued by a lack of a good definition, and crows unlocking puzzles and other animals doing other scraps of smart stuff.
It seems like nonsense to be searching for things without perfectly clear criteria. Don't look for things if you don't know what you're looking for, or at least don't call it "looking for", just call it what it is: "poking around and brainstorming."
Though perpetual motion is reasoned to be false, rather than declared false because statistically we never had any luck trying, or by an exhaustive search of all possible perpetual motion machines.
You're right: you said "statistically we never had any luck trying, or by an exhaustive search of all possible perpetual motion machines." as an antithesis.
I took "reasoned to be false" as sort of a weak and refutable statement.
It's important to tell former from latter. Unexplored things are not the same as things that have been explored and found false.