This situation happens because the flight component of a BAH package is often based on an Inclusive Tour (IT) fare. These are fares that are not allowed to be marketed or sold as a standalone product and are not allowed to have their price disclosed separately. They can share the same buckets as published fares, e.g. booking as a package can access a cheaper "D" fare than a flight-only deal can: it's not necessarily about more availability opening up in cheaper fare buckets.

The same principle often applies to the hotel portion of a package, with the room rate being confidential and only to be sold as a package. It's a great way to generate further sales without airlines or hotels having to undercut their lowest, published rates.... and as a consumer, you can often get a great deal.

I don't actually know if car rental companies make package fares available - but even if they don't it all still works out if adding the car "unlocks" the IT fare.