Are you talking about BHR "services"? If so, they usually do not encourage anything, they simply do what they are paid for.
Not sure what you are talking about when you mentioned "lose on their revenue". Usually, the a BHR service only gains something by having devices being sold in Brazil (they usually gain money in in the importation license, because the cost for registration is low and they usually asks for a fixed pricing for maintaining registrations), so the quicker the registration is done, the better for them.
I don?t understand your comment "If the BRH is a member of the ABIMED (Which most of the BRH are anyway) they would take up the BGMP process as well through the letter of authorization.... ". Yes, if the BHR is a member of ABIMED, they can help speed up the registration process by speeding up the GMP certificate using the ABIMED mandate. This has nothing to do with the MDSAP.
And no, nor FDA or ANVISA will "commit to stop the routine inspection / BGMP audit and instead promote the MDSAP". MDSAP is an alternate route, and it was created basically to help regulators solve their problem of inspection queues.