I think the best explanation I've heard came from Roy Koopa (a board member who used to post a while back.)
It was basically that, a while after Yoshi's Island had occurred, the storcks thought that they would try to get back at Bowser for hijacking the stork and intercepting a delivery. So they planned to send him the most nasty, bratty, troublesome kids that they could manage - seven of them! - to teach him a lesson.
So, these seven Koopa Kids soon arrived at Bowser's doorstep, and the storks' plan backfired horribly. He loved their loathesome traits, and willingly raised them.
Go Moon!