For me, it depends on the snake.
With hatchlings in delis, they are housed on paper towels, so I do feed them right in there, and regularly change out the paper towel afterwards. I've just found that to be easier and less fuss for the itty-bitty ones during their first few months.
Once the babies have graduated onto aspen, I use separate feeding bins until I am comfortable with their feedings habits. (This applies if I acquire new yearling or adult snakes, as well.) Once they have demonstrated solid, consistent grab reflexes off the feeding tongs, generally they are all fed in their bins.
That said, I do have one girl (two years old, I've had her from the day she hatched) that has lazy feeding habits, so she still has a separate feeding bin. I don't want to leave a mouse in her tub and have her drag it all over the place while I'm not looking.
ETA: Even with most of my adults being fed in their bins, I have never had any issues with aggressive behavior. A couple can be excitable when I open up their tubs for regular handling (mouse optimists), but I've never been bitten or struck at while reaching in to pick them up. I'm sure it could still happen, but I don't really consider it to be a concerning issue.