Doing the writing assignment live and on-screen is simply to verify you didn't cheat/impersonate/get help/use AI/plagiarize.
b) Not necessarily, some companies would care if their contract writer stole/copied/repurposed/reused content from a competitor/regurgitated copyrighted material. Think also GenAI hallucinations, fabricated citations, etc. But sure, most cost-conscious companies won't give a hoot, so they could probably get by with cutting corners.