A tapered rod allows a skinnier forend. ie: 3/8" tapered to 5/16" or 1/4" allows a VERY skinny forend on a fine little small bore- .40 or so. A .32 might get a 5/16" rod tapered to 1/4". Thusly, a 7/16" rod tapered to 3/8" for larger calibers - same deal, or even 1/2" rapid tapered to 3/8", like the rod for my 14 bore.
With the larger end sticking out of the pipes & taper starting after the first rod pipe, but the time it gets to the second pipe & then the entry pipe a very strong 7/16" rod for a .50 can be tapered to 3/8"- smaller entry pipe from the rod's taper means less wood needed under the barrel. this slims up the stock, making for a slimmer, trimmer looking rifle, one the barrel and parts grew into, so to speak, not merely added or stuck on. Too, the taper gives the strength of the heavy rod, without it's bulk.
Of course, the gun must be made for the tapered rod as it's being built - in order to take advantage of the rod's profile. Soem folks have difficulty with this, as they just can't go into a shop and 'buy a new, finished rod for their ML gun. With custom guns, it gets more complicated with parts, of course.