I know doll limbs can be tight when new, but I’ve never felt so tight as to cause damage by moving in the way they are intended. You are correct in that as the doll is used, the limbs usually get less stiff and eventually become very loose–at least with the dolls I’ve owned.
It looks like they are made the same as AG dolls. and if so it’s a rubber band holding the limbs in their sockets. Maybe they are just super tight? I had a doll with limbs that were too tight and the feet snapped together if i moved one leg and let go of it.
I don’t have any experience with My Life As dolls, but maybe someone else has and will offer some help.