This pattern is a little awkward in my opinion. The best reason for outing up with the (minor) added hassle of having 2 balls of yarn attached at once, is the benefit of being able to work both shoulders at once (which salmjnmac has mentioned). Personally I’d either attach the second ball and work both shoulders at once, or I would first work the side where the yarn is already attached and leave all the other stitches on hold to return to later. It just seems a faff to have 2 balls attached but then only work on he second shoulder and not the first.
The stitches for the neck that you have on hold, you might want to put stoppers or elastic bands on those needle tips to prevent the stitches sliding off while you work the shoulders. Or you can use a length of yarn as a holder which might get in the way less than the spare needle which might poke into your knitting or tangle with your 2 balls of yarn.