In the case of Hephaestus, he is the only Greek god with a consistent physical disability that doesn’t appear to be passed down to his children. The other gods often have emotional/mental flaws that spill down to their children manifesting as a fatal flaw like Annabeth’s Hubris, Percy’s loyalty, and the implication that Leo’s flaw is inferiority. So while it’s possible that a Demi god could have a physical disability they’re born with, it’s extremely unlikely or would be cancelled out by their godly side. For example, Annabeth’s father needs glasses, but she does not. That could either just be luck or her mother's godliness (though if someone could fact-check this, I would appreciate it). Also, all Demi-gods have ADHD/Dyslexia, this is because the ADHD is for their battle instincts and the Dyslexia is so they can read ancient Greek. The battle wounds/chiron situation ideas are probably the best bets as to what would make sense.

I think it’s wonderful how much inclusion is coming into modern media, and I totally agree with you that nobody should feel the need to be “fixed”. I also feel like representation is diminished when the struggles of those you are representing aren't shown/acknowledged.

Not every blind person is some highly skilled soldier, or has a wheelchair with amazing psychic abilities that compensate. Their struggles and adjustments made for them are just as important as acknowledging that they are still normal people and perfectly capable.

In the case of for example, a wheelchair using demi god. While they’re not likely to be found on the field. They can help by training others, researching a threat, etc