No, chick starter is really no different than an all flock feed, which can't hurt layers at all as long as they get the calcium they need in the form of calcium carbonate (oyster shell).
The problem of soft-shell or shell-less eggs can be chronic or fleeting. An individual hen may have a...
She's okay for the time being. However, she has calcium issues that could cause a repeat of this recent performance. Eggs lacking hard shells are much harder to pass and therefore, they are more likely to get stuck. You want ot avoid this, of course.
I've had wonderful success treating hens...