their big eggs are actually that size for a similar reason to human babies having massive heads!! being bigger at birth can be important.

kiwi are trying SO HARD to become mammals. fur-like feathers, whisker-like feathers, little beady eyes, nocturnal, great sense of smell.... that's basically a mammal!! they're well suited for life on the forest floor.

their big eggs work alongside these adaptations to give them a leg up in the bird world. their young hatch already feathered! they're precocial, which means they're born with the ability to open their eyes and move around. like foals.

big egg = more powerful offspring from the get-go. babies don't need to spend precious time vulnerable while they develop on the ground when they've already done all that in the egg!

That being said... trying to preserve not the rhyme scheme, but even the specific vowels being rhymed, and even the consonants... is kind of doing a little bit too much. And only really pleases the people who are already familiar with the phonetics of the original song. Which arguably defeats the purpose of doing a translation to reach more people... unless you're just doing it for the sake of doing it which is also respectable.