a. I hope it was obvious that I staged that picture for fun (blog post) and that I was not finished with the splice (only a few tucks in).
b. Of course a chain-to-rope splice is intended to go through a
windlass. In fact, this is the splice specified by
windlass manufacturers. That said, I prefer an irony splice, below, for windlass use because it is smoother (which is not what the OP was asking, in my understanding). However, it is more difficult to make well and isn't beneficial for anchors that are hand hauled.
c. Tapering is for strength. The weak spot in both bury and tuck-back splices is the starting point of the splice, because of the bends in the
rope the splice tail causes. Bends weaken
rope. By tapering these bends are reduced. The bend around the chain, oddly, is less important because there are 4-6 strands carrying the load at that point, not just 3. Taper is even more important when splicing high modulus ropes. Absolutely not a matter of cosmetics.