Even if you downloaded all ads in advance and ran all the logic client side, basing ads on chat info would inevitably leak information if the ad was ever clicked.
True but I'm sure they can come up with something. Maybe unclickable ads like "buy dominos pizza, only today 5% off" or "watch NBA on Prime today 7pm"...
Inevitably advertisers will want to measure the effectiveness of their advertising, so "use code XYZ at checkout" will, and "mention this ad" could, still leak targeting information.