That wasn’t the original argument now was it? If you’re going to move goalposts then at least be halfway correct the first time.

Hot water dissolves it much quicker, giving the illusion that it dissolved more. It’s not actually saturated when you’re trying to stir it into cold tea, it just dissolves extremely slowly. If you were to saturate it while hot (which would take an insane amount of sugar), then yes, it would recrystalise. But in pracrice, you need to dissolve it while hot because the more energetic molecular motion in the solution dissolves the sugar faster, since the heat is causing more effective collisions. Saturation point and the change thereof is, contrary to the proposal above, not a factor here, since everything is happening well below that point even with the sweetest teas commercially available.

That is only because it’s not saturated. If you added an ungodly amount of sucrose (and I like it ridiculously sweet but this would be undrinkable), it would recrystalise when chilled. That’s why there’s a controversy here. A saturated solution would recrystallise, but people are pointing out that tea obviously doesn’t do that. That’s simply because no one drinks it saturated. It’s hard to stir in while cold because the rate of dissolution varies as temperature. That’s why there’s some confusing as to thinking it’s about the saturation point. It’s actually below it in both cases (hot and cold). To learn more about that mechanism, read about how reaction rate is affected by temperature.