That would slow down boarding exponentially. It just takes one or two assholes to need to have flight attendants stationed throughout the entire cabin making sure people use their bins.

Rule of thumb: if you are anything past the first peasant boarding group, look ahead. If things look crowded? Find the first mostly empty bin and just put your bag up there so that you can grab it on your way out. Otherwise you are gambling that there will be an opening closer to where you actually sit which inevitably is five rows behind you.

And that (and lounge access and not needing to manage miles for status) is why I ended up just getting the fancy credit card for my airline group of choice. Priority boarding means it doesn't matter where I sit: I have "my" bin.