With a properly set-up Jazzmaster/Jaguar-style bridge system, you can down-tune from standard tuning, and the guitar will still be in tune, and, as a bonus, you can still use the tremolo bar, though only go down in pitch when down-tuned. This also can allow you to keep playing if you break a string in the middle of a song.
Despite the all love, some players complain that the Jaguar doesn’t have the sustain of a Strat, and — from personal experience — it often has this weird string-buzz thing going on. Which is one of the reasons I sold my Jaguar for beer money in 2007 (I did eventually crawl back into this corner of the universe when I bought a Jazzmaster in 2011).
When you're recording, you can use all kinds of exotic instruments for embellishing sections of a song. But you probably would like to be able to recreate your recorded performance live. It would be cool to be playing something on a six-string and have certain notes of the melody jump out with a 12-string sound and attack.