A drink with bourbon and rye makes no sense imho. A rye is just bourbon with a higher percent of rye and less corn. You might as well call it blending your own whiskey.
It guarantees a minimum balance of corn and rye in the resulting blend. If you have a whiskey that you know has an appropriate mash bill (e.g. Rittenhouse BiB) then you could be boring and just use that. But there's also more to a whiskey than its mash bill. Blending different kinds can yield new and interesting flavors. And after all isn't that what cocktails are all about?
This is pretty common in rum drinks, especially tiki. Like you said, rye offers something unique separate from traditional “bourbon” and so the flavor profile of the end drink is different
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Highly suggest making an old fashioned flight to try it out. Choose your favorite bourbon (which has a corresponding rye), and make 3 old fashioned, 1 with only bourbon, 1 with only rye, and 1 with a 50:50 blend. You might be surprised which you prefer.