The phrase "the likes of which" is a somewhat formal and literary expression that means "things similar to what is being mentioned" or "things of the same kind." It is often used to emphasize that something is unique, extraordinary, or unparalleled. While the expression may not be as commonly used in everyday conversation, it is still fairly well-known and understood by English speakers, particularly those who are familiar with formal or literary language. Many people would recognize the phrase and understand its intended meaning, especially in context. However, it's always possible that individual understanding may vary depending on a person's exposure to different styles of language and their overall familiarity with idiomatic expressions. So, while some people may immediately grasp the meaning of "the likes of which," others might require a moment to decipher its intended sense, especially if they haven't encountered it before.

I am a native English speaker and this sentence really makes no sense. If I heard this "town novelty and befuddlements" I would think, what the heck? However, "the likes of which" is pretty common. For example: What an amazing view, the likes of which I've never seen. It just means, the measure of which, or this is the first time I've seen this....

It's immediately understandable to me but what's more noticeable is that the style of language ("this fair town" and "novelty and befuddlements") is telling me that either the event is from 100 years ago or the writer is deliberately evoking an antiquated, formal, and grandiose style. It immediately brings an image to mind of an old timey politician giving a public speech. In that sense, the style choice is successful.

You will never hear this type of language in normal conversation. It is deliberately archaic and verbose [excessively grandiloquent] and is used to attract attention and sound amusing.

I would use both phrases in spoken and written English in everyday and specific situations: and the reasons might be (but are not exclusively) to expand language into the realms of traditional, the literary or the absurd, for the fun of the way it sounds and the reactions it may have on other people. Other writers do it too, so it's something of a convention in modern literature; a way to enliven otherwise less interesting speech patterns with unexpected or playful wording.