As far as I can tell, there are no examples of trapdoor functions which hardness assumptions is merely hardness of some NP-hard problem in worst case. That is, a trapdoor function in which, it is proved that, if there is an PPT algorithm that can invert it with non-negligible probability, then there is a PT algorithm which can solve the worst case of some NP-hard problem.
If I am wrong on the above, can you show me an example of such function?
If I am not, why is it so hard to make such a trapdoor function? Is there a concrete reason why it's hard to develop such function (beside "we haven't figure it out yet")?
This supposedly "duplicate" question (Why hasn't there been an encryption algorithm that is based on the known NP-Hard problems?) doesn't actually answer this question. That question isn't why worst case NP-hard isn't enough to make an encryption out of it. This question is essentially about why there had been no successful attempt at reducing average-case hardness down to worst-case NP-hard, for the purpose of making trapdoor function. There had been problems where average-case is just as hard as worst-case, so the fact that not all problems has worst-case=average-case doesn't mean you can't use different problems where that is true.