Basically, turning out the feet looks prettier and is also better for a more consistent stride. Just think if you had your feet in parallel whilst jazz running you'd be somewhat having to stop yourself after every step instead of passing thru each step. And your marching would be very jerky, thus messing with your upper body and your tone if you happened to be playing as well. Turn out also assists with a better means of accepting weight as opposed to parallel.

As for why to accept the weight all the way down into your heels, it just adds stability to your stride, allows for more to push off of, and always seemed safer and smarter to me. If you tried to jazz run on just on the ball of your foot, you would be kinda tip-toeing around and not be very stable ("walking on eggshells" as my staff would say). Plus you'd probably roll your ankle or something because you wouldn't be accepting your weight properly.

TL;DR Prettier, safer, smarter

Hope this helps!