The locks on my interior doors are all keyed and can be unlocked and opened with just a credit card. Why? And is there a way to fix it? Perhaps that doesn't involve drilling a whole for a deadbolt?

For one thing there is 2 types of terminology that you are dealing with.

1) to pick a lock means to manipulate the locking system to be able to open the lock.

2) bypass: what you are doing is bypassing the lock itself.

The curve of the lock is what allows the lock to hit the striker plate and allow for the door to close. A deadbolt is straight and not subject to the same. So you either need to close the gap so the lock can't be accessed or change to a deadbolt type of system.