I think something a lot of people forget is the meaning and the importance of political marriages.
From a purely political standpoint it makes sense to for Zuko to marry Katara.
1. Royalty needs to marry royalty or other high ranking nobles.
By pure process of elimination: Zuko can’t marry FN nobles due to their involvement or financing of the war. He also can’t allow a pro-war family to slip their daughters into his bed and poison his mind/court à la Anne Boleyn or Alicent Hightower (HotD).
He can’t marry an Air Nomad, the nation most impacted by the war, because there’s none left.
He can’t marry a Northern Water Tribe woman because their highest ranking daughter Princess Yue is dead and NTW noble women are not raised to defend themselves so that’s an assassination attempt waiting to happen.
The Earth Kingdom would be good candidates and they were raised for such courtly life (just look at how Toph was raised) but they were not as badly impacted by the war as the FN’s second biggest victim, the Southern Water Tribe, who does have a “Princess” in the form of Katara, the SWT’s chieftain’s only daughter.
Mai is a good choice as she’s a FN noble from outside the main court as her father is a colony Governor but she’s also the daughter of a colony Governor. It was a tricky situation all around. She proved her loyalty to the Zuko but her background makes her an uncomfortable option for everyone else who would see the position of Fire Lady as a reward to her family/father.
2. Political marriages are how peace treaties are signed in blood.
They make it incomprehensible to attack the other nation when there is shared blood between them. Kind of like Queen Victoria did ILR by marrying off her children to different kingdoms in Europe or what the Starks, Tully, and Arryns tried to do by intermarrying their children in GOT.
A child is the ultimate expression of unity AND a hostage. Children are also a symbolic burying of the hatchet. Politically no one wants to kill children who they share blood with.
3. With a political marriages you don’t just get a seat at the table, you get to sit at the TOP of the table.
If Katara married Zuko she would have access to the FN’s resources, which if she endeared herself to the nation, her new citizens wouldn’t complain too much about her using those same resources to help her nation. It stops being reparations and becomes a symbol of “love”.
Fire Lord Zuko isn’t selling out the Fire Nation, he’s showing his “love” for his wife by helping out his wife’s home. Alternatively the public could also see this as Zuko paying a bride price in exchange of marrying a literal War Hero. The more politically inclined, would also say that Zuko thinking long term. Improving the SWT so that his children have better inheritances if/when they become the SWT chieftain. (Sokka would need to die childless for this to happen but to the FN a little assassination is nothing)
4. Lastly for this political marriage, the Order of the White Lotus is inserting an active threat into the highest levels of the Fire Nation.
Katara is known to be a talented and incredibly dangerous fighter when she’s FOURTEEN. She’s the perfect deterrent for an insurgency because she will NOT hesitate to throw hands only get better with age. Katara also grew up being hunted by her husband and knows all his moves and his secrets. As a healer and a fighter, Katara has all the tools to keep Zuko safe from retaliation (from all sides really) and to put him down if he becomes dangerous.
This isn’t the perfect trope but it adds a level of intrigue that the original material doesn’t give us. It also adds to Katara’s character. She doesn’t take action because they’re easy. She does them because they are right. Marrying her enemy-turned-friend would be hard but for lasting peace, for a chance that her children and grandchildren don’t have to go through what she did? Katara would do it.