I think homework would be fine, it really depends on the person. You can find people with ADHD who would crush these questions and others who wouldn't.

Personally... I had another profession before and was never asked anything during interviews. They just assumed I was capable because I had a degree, work experience and references. So I'm not quite sure where that even is coming from, it's unheard of in other professions.

Some companies want you to describe your solution, or say pseudo code is fine. But not every company will be completely honest about how much they actually do penalize for improper syntax.