It doesn’t imply pain of walking on crushed egg shells. It implies walking such that you don’t crack the shell. “Eggs” by itself doesn’t imply the shell (like some people might think scrambled eggs or whatever). The consequence of not treading with care is crushing the fragile eggshell, or in real terms, emotionally sensitive individuals cracking really easily. Feeling like walking on eggshells is simply stating that you feel the need to practice unreal levels of caution.