Companies don’t gain anything from the take home assignments that the candidates submit. It’s highly improbable that the assignment you submit has the next big idea for the company. Even if the idea is great, execution is a different ball game. A PM’s idea is useless unless it’s executed properly. And if they have a PM who can execute properly, there are high chances that they would have come up with the idea as well.
So the real reason why the companies don’t reply after giving take home assignments is that either the position is put on hold or you didn’t get shortlisted. So either way, you brush it off and move on