How many Avatars do we know of that actually had kids?
Off the top of my head just Aang (obviously) and Roku (Zuko's maternal ancestor.) I don't think there's any mention of Kyoshi even having a husband and while it's possible Kuruk had kids before his wife/lover had her face stolen, I don't think any are mentioned.
Based on that admittedly limited sample size, we can conclude that no Avatar we know of has produced offspring that has shown a bending talent other than that of their or their partner's birth nation.
Myabe that's why Bumi is a "Squib"? He looks like an Earthbender, but, has no bending abilities, maybe because he doesn't come from Earthbending parents?
One Day I hope to be the Man my Cat thinks I am
Where are we going? And why are we in this Handbasket?