Candidates for One-Way Function
Here is a "canned" answer that might be useful, but has no cryptographic depth (hopefully we get answers with depth as well).

What makes for a good candidate OWF? The naive answer tends to boil down to "something that looks hard to invert to me", but the expert's response is usually more like "something that many smart people have tried to invert but failed" (or something whose invertability would imply that of such a function). From this perspective, it is worse for the problem to be more obscure (fewer have tried it), and it may be worse that the function is more complicated (this obfuscates whether it is truly difficult or you just cannot see the solution yourself).

To put the intuition another way, a common "bad intuition" is that if a problem looks more complicated or difficult to define/understand, then it is more likely to be computationally difficult to solve. Theoretical crypto does not accept this premise. The primary evidence we have for computational hardness is a history of failed attempts, which means good candidates should be simple, well-known functions with long histories.