Pokémon Scarlet and Violet might be the first game in the main series where the versions' box Legendaries are not actually Legendary Pokémon. While there's no question that Koraidon and Miraidon are important to Scarlet and Violet, they lack a lot of typical Legendary traits. As a result, one could argue that despite their position in the game, they were never actually Legendary.
Legendary Pokémon have always been a major aspect of the games, ever since Mewtwo and the Legendary Birds in Red and Blue. They're the strongest Pokémon that the game has to offer, and they usually have some impressive lore behind them as well, standing out from all the others. The strongest Legendary trio in Pokémon, Diamond and Pearl's Creation Trio, may be the best example of this, being a key part of the myth of Sinnoh's creation. The other Legendaries have impressive stories of their histories to tell as well, except for newcomers Koraidon and Miraidon.
Scarlet & Violet's Mascots Are Probably Cyclizar's Relatives, Not Legendaries
Koraidon and Miraidon already broke tradition by joining the player at the start of the game. Normally, Legendary Pokémon are late-game acquisitions, with the chance to catch them being something of a reward to the player for making it so far in the game. Granted, Koraidon and Miraidon can't battle when the player first receives them, being restricted to their vehicle form until Pokémon Scarlet and Violet's postgame quest. The climax where Koraidon or Miraidon's true form could be seen as when they are properly caught, but since they had accompanied the player through the whole adventure, that wouldn't be a fair statement.
Another important aspect to Koraidon and Miraidon is their astonishing resemblance to Cyclizar. Cyclizar is a Dragon/Normal-type Pokémon that looks like a combination between a large lizard and a motorcycle, and it's known for letting people ride it. Cyclizar is well-known enough for several characters to use them, which raises further questions about Scarlet and Violet's box Legendaries. Considering their circumstances, it's likely that Koraidon and Miraidon are actually the ancestor and future evolution of Cyclizar, respectively. Pokémon Legends: Arceus' possibly extinct Hisuian forms already showed how Pokémon can change over the years, and Koraidon and Miraidon could be the same. Rather than Legendary beasts, they're likely a part of Cyclizar's history.
Koraidon & Miraidon Are Special Despite Dubious Legendary Status
Even though Koraidon and Miraidon may not be actual Legendaries, that shouldn't detract from what they do bring to the games. They are loyal companions to the player unlike any previous Legendary, and they play an important role in the overall plot line. In addition, even without the possibly world-warping power that other Legendaries wield in lore, the two are still impressively strong Pokémon that are effective mascots for their specific generation. Even if one agrees that they aren't Legendary Pokémon, it's hard to deny that Scarlet and Violet would have been far different games without them. SV's Koraidon and Miraidon may not make sense, but they're an iconic part of the game nonetheless.
There's a decent amount of reasons to suggest that Koraidon and Miraidon are simply from the past and future rather than proper Legendaries, and that's just fine. They're still an important part of the games even if they aren't on the level of past box Pokémon. At the end of the day, Pokémon Scarlet and Violet's signature Pokémon might not be proper Legendaries, and don't need to be.
Source: Nintendo of America/YouTube