First off it seems very odd that the backorder option isn't available unless stock management is enabled on the inventory settings page. I should be able to use the backorder feature even though I'm only stating whether a product is in or out of stock (stock status).
Secondly on the product page Stock Qty and Stock Status should not be shown at the same time since they're mutually exclusive.
What I'd expect was the option to select Stock status and combine it with a backorder option. For instance "Out of stock", "Allow, but notify customer" and then get an "Available on backorder" on the product page with an add to cart button. Currently it shows Out of stock no matter the backorder settings.