Doing the writing assignment live and on-screen is simply to verify you didn't cheat/impersonate/get help/use AI/plagiarize.

Contract implies they hire a service, thus should not care how it was created, right?

a) Outright cheating in the interview is probably a bad sign about the candidate (whereas the interviewers might be ok with, say, using GenAI, which is increasingly common in many sectors). But impersonating a candidate, or having a friend sit in with you, would always be a bad sign.

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.

I interviewed for a Sr Software Engineer gig there in 2022 and had a laughably negative live-leetcode experience where the interviewer was visibly zoned out almost the entire time and mostly just awkwardly stared at the camera while I found a solution - whether or not the most optimal, I guess - to whatever pointless never-going-to-actually-write-stuff-like-this-on-the-job thing they'd asked me.

I asked for feedback on the blurb or ways to improve it and got told, basically, "well you took so long" (~30 minutes?) "to implement this that we don't really have time for that", or something to that rough effect.

I got a relatively generic rejection email shortly thereafter, and frankly, only minded because I was unemployed at the time. I have no idea what whoever designed their hiring process thinks they're getting out of being overcomplex and generally cold, but I can't imagine it's anything good.

Seems like it worked for them.

Yep, attracting a reputation as a shop with a joke of an interview process seems like a good achievement to strive for...