There was lively debate on this topic when the Snowdonia NPA asked for comments at a BMC regional meeting.
Those most against the idea (or preferring a simple 'code number' system rather than GRefs) were outdoors education providers, concerned that it will make setting navigation exercises impossible because students will be able to walk to the nearest stile rather than bothering to take bearings on distant landmarks.
Personally I would look at this the other way round - for instance with kids you would be able to ask them to work out the GR of a stile first, then get them to go and check their answers by looking at the tag.
The system is, I think, aimed firstly at the NPA being able to identify each piece of 'furniture' in the mountains, so that it's easier to report and arrange repair of broken stiles / gates etc since logging the precise design/position of each will be easier.
As for being a 'navigation aid' - there are certainly times when I have become misplaced in the mist and although I'm pretty sure of where I am, and can develop a navigation strategy to allow me to avoid any dangerous obstacles while I find a locatable landmark, the ability to locate, for example, which of 3 stiles along the length of a fence I have just reached may well be beneficial or at least comforting that I am where I think I am.
More importantly, if someone without any map skills who is lost on the hill can find a stile/gate before phoning for help, the MR team will be able to locate them far more quickly and in many cases may well be able to advise by telephone on the correct route off the hill (e.g. just follow the fence downhill and you'll soon reach the road) or to safety (go 100m up the hill and there's a sheepfold, shelter there while you wait for the rescuers), rather than having to send out a search party (or rely on phone signal accuracy) to locate them first.