Putative Should

would someone please be kind enough to explain more about Putative Should for me?

I read about it in this article but it seems like I can’t find any other sources to learn more about it. almost all the pages I visited were referring to the same one.

https://www.thoughtco.com/putative-should-grammar-1691554

my questions are:

1. Is it still common?
2. as I read it’s only for BrE and not AmE, is that true?
3. can it be omitted?
4. can it be used with only few known adjectives or almost all adjectives expressing emotions?
5. I also don’t see how these two examples can be the same:

A. It is sad that you should talk such nonsense.

B. They insisted that I (should) stay the whole week.

in my opinion B has a sense of obligation in it but the same doesn’t go for A.

I would be so grateful, if someone could help me with it.