This is a good mathematical analysis. But here's another way of looking at it: the hot hand fallacy is stating that every shot is strictly independent. You don't have good days and bad days, every day is exactly average. Which is ridiculous, especially in the negative direction:

- A player could be sick

- A player could have an minor injury they are playing through

- A player could have not eaten properly before the game

- A player could have been practicing a new shooting form and not quite adjusted properly yet

If you can have bad days, by definition all the other days are good days even if they are only "normal" days.