It's an accounting simplification.
The accountants want to say the item's book value is now $0 (because they can use the loss for a tax break). Destroying the item neatly proves this claim to any auditors, because if the wasn't actually worthless, it is now.
If there is any suggestion that the item should be donated, then it wasn't worthless. It has some value to someone.
This doesn't make donating it impossible. The accountants would just have to update the items book value to its current real value first (they can still count this decrease as a loss). But how do you work out the current real value of the item? You need documentation justifying this new book value that's good enough to satisfy any auditors, and such documentation might be expensive.
I believe most tax codes even allow you to claim the real value of the donated item as loss (as long as it's a registered charity), so the overall tax break should be identical to destroying the item. But the extra time and paperwork makes it much more appealing and cheaper to just take the simple option of just destroying the item, especially when the accounting department is short staffed.