Me too. Also, I don't want to do some work for "free".

I'd prefer to see it as an investment in yourself, so not really for "free". Also it's (probably) not like the company will make any money of the home assignment they give you.

The company makes money off of using this as a candidate screening tool in lieu of in-person engineer hours.

The fact that a company is cutting costs doesn't mean it is "making money". Nothing is being offloaded, it is just a process that doesn't require one of their employees to be present.

I think it is better for everyone this way. It is more accurate, it is less pressure and less demanding on the candidate, and it doesn't require an engineer sitting there asking intro-CS questions to a stranger instead of working.

They're likely not. Not only would they need to have a different question for each candidate, which kind of nullifies that being able to be used as a neutral judgement, but the code produced likely won't pass whatever internal code and style guides are used in the team and would need to be refactored to actually be used.

You're doing homework either way: either take-home project homework or cram-before-interview homework.