We tried that once and it failed, because the median random submission is so much lower-quality than the rest of the frontpage. People reacted much as they would to finding kitchen compost in their breakfast cereal.
Maybe this could be an option to enable in profile settings?
I definitely think this is a good idea for a new social platform, though. Probably the key is setting expectations correctly.
I do wonder if a new post quarantine box on the front page, marked as such, would do better than just mixing them in.