Assorted problems with Chesterton's Fence:
Our ancestors were paperclip maximizers, so even if the tradition served their goals, it's not that likely to serve ours. Think about how different you are from your parents, and the generational clashes and changes just in the past several decades. How much do you think you have in common with an ancestor from the 19th or 16th century?
Existing traditions are optimized for survival, not quality. If your society practices a tradition in an environment roughly like the one in which it developed, it probably won't go extinct - but that's an extremely low bar! It doesn't mean anyone's life is better for following it, and if you think you can do better for yourself by disregarding it, you may well be right.
Communism is the common Chestertonian counterexample - "It seemed like a good idea for legible reasons,", they say, "but it turned out to be so horrible, it killed a huge number of people! Better to stick with our illegible traditions.". But there were legible, non-traditionalist reasons (e.g. standard liberal arguments, neoclassical economics, the calculation problem) to oppose communism even before its famous famines/atrocities.
A tradition might never have served a useful purpose at all, if it was perpetuated as a mark of group membership. ("If you want to set yourself apart from other people, you have to do things that are arbitrary, and believe things that are false.")
If a particular tradition is good, it can be justified on its own merits, without appeals to Chesterton's Fence. The case for it isn't necessarily persuasive, but that's a problem for any argument, not just for keeping traditions. That's a reason to double down on explicit, legible reasoning to make sure you get it right, not to set it aside for "Well, it didn't kill our ancestors...".