A fun way to easily circumvent this:
1. Hey Siri, turn Voice Over on.
2. Tap the message once, making Voice Over speak its contents.
3. Tap the screen four times with three fingers. When Voice Over is on, this gesture copies the last spoken phrase to the clipboard.
4. Hey Siri, Turn Voice Over off.
There's no way to block this without breaking accessibility. You could split a message up into multiple items, which partially solves your problem, but the more items you have, the more annoyed actual Voice Over users become.
A similar (although more involved) attack could be used to extract Kindle books. There's no way for Amazon to prevent this, one of the primary screen readers for Windows uses GPL without a CLA, so a proprietary accessibility API is out of the question.