The biggest advantage to me is the location of the weight. Crampons are pretty heavy and placing them on top of my pack, near my back makes for a much nicer carry. You can experiment; pack them close-inside and then pack than far away from my center of gravity. You can feel the difference.
A couple more advantages in no particular order:
I like to have a ‘clean pack’ nothing on the outside whenever possible. This has numerous advantages. I will even carry my ice tools in my hand or, if I have the space, I’ll put my ice tools inside my pack as well. The only time I use the ice axe carry straps on the outside is when I will need the ice tools really soon or the pack is just really full.
It protects other people and objects from the sharp points. Especially important in a cable car or your friend’s new car.