The question has two parts - "is there a way to define closeness of geometric objects?" - which is the kind of question that mathematicians ask and answer all the time - and "using that definition, how do we find the closest shape?".
There are many cases of this and it's a contentious issue, these questions often get closed and I don't think it is crazy to do so because what they are literally asking is unclear. However implicitly they are asking "how do I make this question precise, and what is the answer to that precise question?".
How should we deal with such questions?