Shouldn't vs should not usage

Solution 1:

As you have noticed, contractions like shouldn't are not the same syntactically as their full versions.

Syntactically, shouldn't etc. behave like auxiliaries (eg should): they precede the subject when there is an inversion (eg in questions).

Should not is not one word, and does not behave like one word. The should is the auxiliary and precedes the subject when there is an inversion. The not is another part of the verb string, normally following the first auxiliary (I am not seeing him; I will not be seeing him; I should not have been seeing him), but in inversion it follows the subject.

Solution 2:

The word order "Should not it be" is not incorrect, but it is a bit dated. The contraction however remained out of convenience, and it's not intended to be expanded directly. This is not at all an exception. For instance:

Couldn't it be...

Hadn't it been...

Wouldn't you have...

None of these are idiomatic when expanded in place.