grammaticality - Why is "not as ... as" preferred to "not cheaper than"?

In the rephrasing exercise

A is more expensive than B. > A is not _________ B.

The only correct answer is supposed to be "A is not as cheap as B".

However, a student suggested "A is not cheaper than B".

In Portuguese, that's a perfectly possible construction, but, to me, it sounds awkward in English. However, I cannot explain why (except for the fact I'm sure I have never heard or read such a sentence - but, again, I'm not a native English speaker).

I've checked all my grammars, but I couldn't find anything that could help me explain to the student why not as ... as is preferred to not more/-er than. What can't be overlooked is that I have found no exercises or examples that allow for the not more/-er than structure.

As it is, I'm not even sure if the sentence is possible (even if it is awkward) or if it is absolutely wrong. Whatever the answer, the main problem remains: why? Is it because of the negative to be? Does it require the as ... as structure?

Answer

This is an entirely grammatical phrase, though not as idiomatic as A is no cheaper than B. However, it is not an acceptable answer to the exercise because the meaning is slightly different. A is no(t) cheaper than B could mean (it even suggests) that A and B are the same price.