The Goq,
First, for a parable to be meaningful, the symbolism should match the reality. When Dovid Hamelech ensured that Uriya haChiti was killed in battle so that he could marry Bas Sheva his wife, the prophet Nosson came to him with a parable that a rich man who had many sheep wanted to make a party, and took the single, beloved ewe of a poor man to use for the feast. The feelings of the rich man in this parable are a good match for the feelings of Dovid Hamelech. In your parable, however, I don’t think collecting fancy eggs is a good match for children.
First, there is no comparison between the desire for objects and a couple’s desire for children.
Second, there is no chiyuv to collect fancy eggs, wheras there is a chiyuv to have children.
Third, in the lens of Torah, fancy eggs bring no benefit to the world (unless they are used for a mitzvah), whereas a child is a new world brought into being.
Now regarding your conclusion, I disagree strongly that the egg was broken as a result of the couple having too many eggs. The egg broke because the couple was careless with their egg. They could have had one egg and broken it.
I have seen some families struggling to cope with just one child. I have seen others running smoothly with many children. The health and safety of a home has much less to do with the number of children than it does the efforts and quality of the parents.