It's not about sharing. It's about having the right supplies when needed. In preschool and kindergarten it's communal supplies. After that, each kid has to be responsible for his/her own supplies and keeping them in his/her desk. If you lose two entire boxes of crayons on the floor, those either go in the trash or in the lost and found. So, you go to do your project and find you've only got 5 crayons left in your desk. Pretty hard to do the work. And I don't think it should be the responsibility of the kid sitting next to mine to share all of his/her crayons with my kid when mine can't keep track of supplies.
And I know if I had sent 6 boxes of crayons there still would have only been a small handful left after a few weeks. But with initials on the crayons they can actually be found in the lost and found. Same with pencils. When all the pencils were lost in a few weeks you have to use the lost and found bucket and those were pretty awful looking -- chewed on, no erasers.
I guess I just see it that labeling was a tool that enabled my kid to take more responsibility. When a supply was lost, there was hope of findng it again. With no label, might as well throw the supplies in the trash because that's where they were ending up anyway. And once I gave that tool, the responsibility followed.