For my part, as a Black American, I don’t think the role of Fire Lady is inherently oppressive either. I think the controversy boils down to a few things:
1. Broader discourse about whether zutara is a colonization fetish ship
This one gets tossed around by antis all. The. Time. Personally, I think it's a disingenuous reading of the ship that disregards their character arcs. It would be one thing if Zuko was actively perpetuating the Fire Nation's war effort, but that is never his motivation. All of his actions in season 1 and his betrayal at the end of season 2 are motivated by one thing: a child's desire to go home. When he finally gets his wish, it only takes him a few weeks to decide to join the gaang because he realizes that what the Fire Nation is doing is wrong. His reign as Fire Lord is characterized by a decolonization agenda that pissed off a lot of his own citizens. It's even canon that he devoted a lot of his efforts toward reparations and rebuilding the southern water tribe!
2. The recency of the Fire Nation’s genocide against the southern waterbenders
Even though most of the southern waterbenders were captured/killed well before Katara was born, her mother was killed as a direct result of the campaign to eradicate them. The timeline we're working with in this situation is much shorter than the gap between the abolition of slavery in the US and Obama's election or between your other example of a Nigerian British PM between 1960-now. The logic here seems to be that because the events in ATLA are so recent, Katara would face more backlash from the Fire Nation people and be forced to shrink herself to avoid ruffling feathers as a result. I think this is a fallacy. Even though slavery had ben abolished for over 100 years in the US by the time we got Obama, he and his family were still targets of virulent racism for his entire 8 years in office. I don't think that any theoretical backlash Katara would face would be worse just because the wounds are fresher; these are problems that don't just go away with the passage of time.
As you astutely pointed out, Katara wants to help anyone who is suffering, including citizens of the Fire Nation as seen in The Painted Lady. Even after the people Jang Hui discover that she's a waterbender and turn on her, she addresses them firmly and changes their minds, then continues working alongside them to improve their lives. Sounds like world leader material to me!
3. The idea that Katara would have no agency or purpose outside of producing heirs as Fire Lady
We know next to nothing about what the Fire Lady's actual responsibilities are in canon. What we do know is that Katara is a compassionate & inspiring leader, Zuko is committed to atoning for the Fire Nation's crimes, and they work insanely well together. It's not hard to imagine that if they were to get married, Katara would redefine what it means to be Fire Lady and Zuko would support her 1000%. She's never backed down from a fight, and he's never taken the easy way out once in his life. With their powers combined, I'm sure they would be able to weather any challenges they faced from Fire Nation citizens or anyone else.
Plenty of people don't like the idea of Katara being subjected to the scrutiny and bigotry that would likely come with leading a foreign country, especially an imperial power, and I get that! But to say being Fire Lady would be "oppressive" is a bridge too far imo.
