…
She set a tone at the very start when she walked right into his space to shake his hand and made him almost pull back into himself in response. She was in charge and never stopped being in charge.
Harris also managed what neither Joe Biden nor Hillary Clinton nor any of the 2016 Republicans managed to do which is successfully bait Donald Trump and get under his skin. Within a few minutes Trump was visibly angry and not in a way that empowered him but in a way that made him lose focus, go down rabbit holes and generally go off onto damaging tangents. Spittle anger, not righteous anger, shall we say.
So let’s say she corrects him on a lie. Then what? Correct the next one? The one after that? The one after that? Trump had more lies than Kamala had time.
Responding to lie after lie after lie just lets him control the conversation. What she did was the best option available.