Winston,
It looks like Boris and Pete have done a great job of covering most reasons for grafting figs.
The one other reason I thought of is this. You need less material to get a whole new tree started by using grafting. If you have a treasured variety and very limited material to work with, you can increase your odds of success by dividing the scion into a number of smaller pieces. In my personal opinion, grafting fig scion is easier than getting a cutting to root. This is based on my personal experience and others may not have had the same results.
I haven't fully tested this out yet, but I have a strong hunch that we could successfully graft a piece of scion and place an air-layer on the root stock, below the graft, at the same time. My theory is that you should be able to remove that air-layer, with the new graft (and new rootstock) attached and pot it up by the end of the same season. Thus establishing a fully autonomous tree in one season while still leaving the rootstock mostly in tact. The hope being that the rootstock will be fully ready for grafting again by the following season.
I'm also one of those guys who's currently experimenting with "less vigorous" scion being grafted onto "more vigorous" rootstocks. To date, I had been using whatever tree I had available as roostock. In the future I plan to use just one or two varieties that seem to do exceptionally well in my local conditions.
I have one unknown variety, for example, that is both a vigorous grower and seems to be cold hardy to boot. The starts I have of this one also came from one of the largest trees I've found in my zone. This tells me at least two things. One: It is cold hardy at least to some degree. Two: It has enough vigor to rebound to great heights even if it may have been killed back in one season or another. I plan to propagate this one as much as possible in order to acquire several well established rootstock to work with.
I look forward to sharing those results as time goes by.
Sorry for rambling on in your thread Winston :-/ .