With Ozai still in charge, Zuko is not going to get /that/ rewarded. It's canon that while the heir to the throne must be related, the current Fire Lord can choose their heir. And even if Zuko is welcomed back, Ozai is going to name Azula his heir. Assuming Ozai doesn't find some reason to kick Zuko out again or have him die in some way. He hates this kid so much that letting him back for a short time is just so he can take joy in the boy's face when it's all ripped away again.
I go by historical succession situations and how delicate they are. Just some examples:
When Charles IV of France died childless, the throne should have gone to his sister Isabella, and by extension her husband... But she had married the King of England, so the French nobility used a vague precedent to exclude her and her descendants and give the throne to the Count of Valois (a cousin) instead and attributed it to the Salic Law. This is also the main cause of the Hundred Years War, because of course the brother-in-law wouldn't give up the throne.
After the Battle of Azincourt, a treaty disinherited the Dauphin Charles from the French throne and named instead Henry V of England as the successor of Charles VI of France... Except Charles VI was insane, and a regent was said to not have the authority to change the succession. Furthermore the treaty named Henry V specifically but he died before Charles VI by a few months, leaving the Dauphin Charles and the BABY Henry VI as equal pretenders until either could be anointed in Reims (Charles couldn't as the city was in English hands, but Henry was a baby and the King of France had to be knighted first and that had a minimum age. Charles was anointed as soon as Jeanne d'Arc liberated Reims).
When Henry III of France died childless, the main line of the House of Valois went extinct, and the succession law made clear it now went to the head of most senior branch of the Capetian Dynasty, that is Henry, the Duke of Bourbon... Except he was Protestant (specifically Huguenot) and France was a majority Catholic country in the middle of the French Wars of Religion, so half the country, including Paris, rebelled and invited the Hapsburg enemies in up until Henry converted to Catholicism (and he was open on the fact he only did it for the throne), at which point he was FINALLY accepted as King Henry IV and the country rallied around him against the Hapsburg invaders.
When the Spanish Hapsburg went extinct, the closest relative and obvious heir was Louis XIV of France, the Sun King himself... Except he was the King of France. Cue civil war that the French won, putting a son of Louis on the Spanish throne... And excluding him and his successors from French succession.
In Russia in the 18th and 19th century the Tsar or Tsarina could choose their successor among their family, though it was generally understood it should go to the eldest son barring extenuating circumstances. Then comes Catherine the Great, who considerars her son Pavel inadequate and instead favors her grandson, and Pavel's son, Alexander. Everyone knew she planned to skip Pavel, that she had confined to the Gatchina palace, but the traditional forces were so opposed that she put off writing her will down until she died, at which point half the palace started looking for Alexander before Pavel could come back from Gatchina... Except Alexander, who was indeed the better heir, respected his father and knew he would become Tsar either way, so he literally hid in a closet near the entrance and only came out when his father arrived, at which point he popped out and kneeled in front of him, effectively making impossible for Pavel to be skipped. First thing Tsar Paul II did was to change the succession law to male primogeniture.
With this historical precedents, I do expect Ozai to treat Zuko as his heir, especially after he came back after apparently killing the Avatar, until and unless he gets a valid excuse to disinherit him without causing a civil war between Zuko's supporters and Azula's. He had got lucky once when Zuko screwed up at the Agni Kai and acted "cowardly" (had Zuko fought back, Ozai would have had to keep him), and after he completed his task Ozai needed another excuse.
tbh Ozai does actually have an excuse in his back pocket to disinherit Zuko from the throne: questioning their biological relation.
There is a letter hidden in the palace, written by Ursa, that says that Zuko isn't Ozai's son. And while Ozai knows that it's a lie that Ursa made up to catch him reading her mail, he could easily present it as fact and make everyone believe it to be so. It's not like they have DNA tests in their world to prove or disprove.
