While I don't disagree with you, I still believe there are necessary differences between the game and real life. If not, we'd all be disqualified once we ran out of a particular ball during the course of a round. Since WGT allows us to continue play with starter balls, then surely they could also allow us to continue play with a ball of our choice, given that it's already in our inventory.
Perhaps it all comes down to what's easier to implement on a programming level - automatically select a replacement they know we all have, or stop game play, allow the user to edit their own equipment (but only the balls), and continue on. Sometimes the simpler solution is just that... simpler.