It looks like the billing address restriction was a "thing" years ago, but is simply too impractical for modern day e-commerce. People want to do gifting, or get things delivered to temporary accomodations like vacation spots. They are relying on approaches like heuristics (sudden purchase for something expensive going to an unusual address), plus CVV verification to help ensure that the purchaser physically has the card (still allows theft, but adds a layer).

No, it was never a "thing," "mark as gift" has always been an option on Amazon to send gifts to family and friends.