Thinking about it, being the Water Avatar after Sonam probably would have sucked big time.
I say this as, we see in the comics, when Aang cuts his connection with Roku, it disrupts his connection with his other past lives as well, making it harder to connect with them than it would have been.
imagine if something similar happened due to Sonam‘s actions after her death, preventing the water avatar after her from not only connecting with her, but also the other avatars before her would have a hard time being contacted.
that would be so bad for the new water avatar, especially as the world is just starting to form the map and world we all know and love from the original series, and the conflicts and politics would be wild, all with struggling to even connect with their past lives for advice and having to figure things out mostly on their own.