The key reason is temperature control. Keeping tempura batter extremely cold is one of the most important techniques for achieving that light, crispy coating.
Here's what's happening: when flour mixes with water, gluten starts to develop — and gluten is the enemy of good tempura. It makes the batter tough, chewy, and heavy instead of delicate and shatteringly crisp. Cold temperatures slow down gluten formation dramatically, so by adding crushed ice (or ice water) you're buying yourself time to mix and use the batter before it gets tough.
There's a second benefit too. When that ice-cold batter hits the hot oil (usually around 170–180°C), the extreme temperature difference creates rapid steam expansion, which is what produces all those tiny air pockets that make tempura so light and lacy.
This is also why experienced tempura cooks follow a few related rules: they mix the batter at the last possible moment, they deliberately under-mix it (leaving lumps of dry flour is fine), and they sometimes even chill the bowl and the flour beforehand. It's all in service of the same goal — keeping gluten development to an absolute minimum so the coating stays whisper-thin and crispy.