Our company is both a customer and a supplier so we see the food safety work from both sides, so to speak.
As a supplier we find it really tiring and time consuming when our customers asks us to fill in several questionnaires (feels like thousands of pages, sometimes) and send in copies of our BRC/HACCP documents. This despite our BRC certification (and other certifications). Firstly, most of our documents are in Swedish, not many understands this language and translating everything is not an option. Secondly, we are annually audited by BRC auditors and external auditors (for internal audits) so we don't really have time for all our customers to perform audits every year as well, that's why BRC Global Standard exists, is it not? 
(of course, we still have customer visits and some even do smaller audits, but it's generally only key customers).
As a customer we have routines that if the supplier is certified according to a GFSI-approved standard only a handful of routine questions need to be filled in like company information, if allergens are handled, social responsibility etc. Things not normally covered by food safety standards. This along with copies of certificates, product specifications and CoA is the basis for our initial evaluation. After a year we re-evaluate after their performances, quality of products etc.
