Sometimes it's not enough protein, could be boredom, maybe your nestboxes are too light, or maybe this bird just likes eggs, it's not normal behavior, you could try darkening your boxes, I would add lots of ceramic fake eggs or golf ball sometimes just trying to peck these items will make a bird give up after awhile, I have heard people putting mustard in eggs, and various concoctions that taste bad. I would certainly try changing some thing before culling, the only egg eater I ever had was a sex link hen, I think it was a lack of protein, you could try putting them back on a grower with higher protein, just some thoughts.