What makes you think anybody is only interested in "Why was the fence built?" and not these other questions?
I think these are all good question that Chesterton thinks you should be asking. The point is that the one who tears down fences or ceases maintaining fences without asking these questions is a fool.
again, you’re putting the burden of proof only on the person who wants to change.
Why isn’t it also an equal obligation on those who want to maintain the fence to justify that? Keeping the fence is not free of costs.
Implicit in Chesterton’s parable is the idea that those who preserve things have understanding, while those who would change things do not. That is why it is seen as a conservative parable.
The point is that you can't make an informed decision about whether or not the status quo is a good idea unless you understand the reasons behind the status quo. If you don't understand the reasons behind the status quo, your opinion is worth diddly squat one way or the other. That applies equally whether you are inclined to keep the status quo or reject the status quo.
So, to me at least, the parable isn't about privileging the status quo but about making informed decisions. Someone who assumes the status quo is without merit is not making an informed decision.
I think these are all good question that Chesterton thinks you should be asking. The point is that the one who tears down fences or ceases maintaining fences without asking these questions is a fool.