Why and how does the egg white stick to its shell when cooked sous vide?
It is because the outer most layer of egg white is not firm/tough enough to survive being peeled without ripping apart. 

If you do not want to ice and boil it, you can torch the outside of the egg for up to a minute. This will cause localized boiling under the shell and physically separate the egg whites from the shell wall. 
Also, overcooking the outermost layer of egg whites will help the egg hold its shape for the softer styles of eggs.