Unless you're collecting the discarded HDDs round the back of MI5, GCHQ, or your friendly neighbourhood financial institution or other organisation with lots of juicy data, the chance of getting enough off a discarded drive to recoup the cost of salvaging it & searching is probably too low to make the effort.
Therefore, I reckon the only people likely to actually look at it are recyclers, looking to see if it's recoverable for less than they can sell it for, & any visible physical damage is going to lead them to bin it immediately.