The usage of "let alone"

Recently, my English tutor pointed out that I misused the phrase "let alone" in the following sentence:

Such high level of publicity of shame notions at different levels is very rare in other Asian countries, let alone in Western society.

By "let alone in Western society", I mean that Western society has even a lower level of publicity of shame notions than other Asian countries. While I was reviewing my document and reading other posts about the usage of "let alone", I don't believe that I understand this phrase thoroughly.

Could anyone help elaborate why "let alone" isn't correctly used in this sentence?

Do you think "let alone" is an informal phrase that should not appear in academic writings?

Clarification based on comments: I remember my teacher explained the usage of let alone in this sentence:

He bought her a diamond ring which was huge and sparkly, let alone expensive.

I didn't take detailed notes about this, which I regret, but it seems "let alone" means a greater extent of what is described in the first half of the sentence. For this same reason, I am now confused about it while reviewing my document a week after the discussion.

The context is shame is commonly mentioned in countries like China and Japan, but not so much in other Asian countries, whereas in the U.S., shame is extremely rarely disclosed or publicly discussed.