Why would they want to police it? Surely Twitter is perfectly fine with you posting screenshots of things of interest (obviously within obscenity and legal restrictions).
I don't know. Twitter reposts of TikTok videos seems ubiquitous, but it seems like TikTok is still thriving. I don't think the primary reason people post a story rather than a permanent post is that they want to ensure the story only lasts for a day. At least for Instagram, I think it's more about keeping your main feed highly curated while still being able to hammer out tons of stories.