Once you've discovered Sky Haven Temple, Delphine Jend tells you that if you'd like to expand the ranks of the Blades, you can bring followers to her, and she'll administer the oath and induct them into the Blades.
What's the benefit of this? Is it just the 'upgrade' to their default equipment? Or do their 'tagged' skills change at all?
The only other benefit that I can see is that for those followers with out of the way or inconvenient 'homes', you can relocate them to Sky Haven for much easier recruitment. This is particularly handy for the Khajit caravaeer I suppose.