She may indeed be tired of mothering because she's been doing that since her own mother died (and I think meta highly underconsiders that her struggle with her mother's death isn't only because she loved Kya so much/more than Sokka loved her, but also because Kya's death reorganized Katara's duties, obligations, responsibilities, etc. to fill the role Kya left. Sokka himself explicitly emphasizes that he sees Katara's face when he tries to remember their mother, which is so heartbreaking because he confirms that Katara, his little sister, became his caretaker. Sokka repeatedly insinuating that Katara grieves their mother too intensely after all this time, implicates an astonishing ignorance that he, the great and smart strategist, fails to connect the dots "I accepted my little sister as caregiver" and "that may contribute to her grieving in ways I wasn't subjected to because Katara filled the caregiver space of our mother for me but no one filled it for her." He doesn't even express any of that to Katara directly, but to Toph and Katara only overhears it by accident!), but both as wife of Zuko or Aang, motherhood is practically a non-negotiable expectation. 

I mean, if anyone really cared about Katara having a loving relationship and the option to have or not have children without all the pressure, Haru would be the obvious choice. Not that I'm super invested in that ship, but he's a compelling counterexample to examine how both Zuko and Aang absorb Katara as a person. "Avatar" (and "Last Airbender") and "Fire Lord" will always overshadow Katara in political significance. Haru has no title, no office, no political/religious function to fulfill; he's just a young man from the Earth Kingdom whose mother runs a shop and whose father is a veteran.

Haru isn't the Fire Lord who needs an heir, and the earthbending population is very stable by the end of the war. There's no structural pressure to make babies, so for them, starting can be a genuine choice they make together, relevant only to them and their immediate communities.

However, more importantly, Haru and Katara meet through occupation, prohibition, grief, fear, resistance, and family loss. Katara bonds with him through what suppressing earthbending is doing to him because bending is also deeply tied to her own identity and history. She sees his community suffering under domination, refuses resignation, deliberately creates conditions for resistance, fails once, adapts, and eventually helps ignite rebellion. Haru saw her doing it; Haru and his father Tyro credit her as the person who reunited and radicalized them into resistance fighters. They are the first men in the franchise who treat her as a political actor in her own right.