some years ago I had to take a break from my startup to consult, partner had a consultant come in to do some stuff, consultant wanted to redo a bunch of things to their liking - one of things he redid was to redo how products were found to be based on navigating by brand - without evidently taking time to consider that many sources of data we had, had a very poor understanding of what constituted a brand and that a brand might very well be some escaped xml and unreadable unicode glyphs, the letter A, the exact same text as the product name, the word Shirt, or a number of other things, including in some instances the actual brand.
In other words he did something because he thought it was okay to do it, he did it because he didn't like the way it was done, but he did not consider that in this case there might have been a reason why it was done the way it was and not the way he wanted it.
There were many things he could have changed, and improved things, but since he didn't bother finding out why things were they way they were changing things for the better was at best a random outcome.
I most commonly apply Chesterton's Fence in the context of new employees / managers. In that instance, it's more about naivety or ego ("I know better"), and less about needing to read the ancient runes to fully understand something.
I've seen so many people jump into a business, want to prove themselves, and start changing things without understanding the context in which that thing was built. (Similarly, though less often, businesses expanding into new products or markets.) "Tell me what will change if you stop doing X" is thus added to "Tell me what will change if you start doing Y".
To be fair, citing Chesterton's Fence just make me sound wise (and/or a little curmudgeonly); the better story for the point I'm making is the hospital bed where someone dies every Thursday morning at 10am ... only for video footage to reveal the cleaner unplugging machinery to plug in their vacuum cleaner every week.