underfire,
I, too, am somewhat surprised by the variety of answers.
Until recently we did not correct FAF. Now we do. The training department had a change of mind and I am quite sure they are knowledgeable about the AMC, the Boeing SP and general procedure design. What led them to that change, I do not know. I am still unsure as to why this is a big thing? We're putting the plane back onto a 3 degree path. Not that we need to, but we do. Correcting the DA is often no more than 50 ft, even on the coldest of days. If it's not necessary, as per procedure design, fine. Then we're just erring on the side of caution.
Come to think of it, we used to have slightly different SOP for NPA-approaches (VOR, NDB), LNAV, VNAV and RNP AR. It was confusing and standardization was poor. Now we fly them the same way whether it's a VOR or RNP AR. It's a valid argument, I'd say.
The MSA is part of your mental map of where you are. I don't go into Chicago, or New York, in blizzards with tight layers of traffic. Many of our destinations are fairly remote places, with terrain and cold temperatures. Separation to other traffic is not a factor. Descending procedurally on a FMC guided path is. Not correcting could be right out suicidal. And I am talking in general terms, not specifically about the VNAV approach.