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.
I remember this being discussed a while ago and I proposed a box at the bottom with a few pseudo-random /newest links. Bu someone raised issues with the idea.
This is what worries me. If too many people read these pages the mods might think it undermines the quality of the community and discourse and just remove them. There is only one acceptable way of using HN, and it's in the service of maximizing civil, intellectually curious technical conversation, and suppressing everything else.