>Doesn't a take-home task also prevent any chance to ask questions in the middle?

Probably yeah. I don't remember my last take-home assignment having communication between the start and the end, although I would have probably been able to send them a question if there was something unclear.

>don't most day-to-day jobs have a large communication component?

I wouldn't know if mine has a "large" communication component, especially in terms of synchronous communication, since everyone's remote, choosing their own hours and so on. A lot of our work is very independent.