In Nathan-Turner's words, 'When the writers rely on it to get out of every tight situation, there's no suspense, no variety. No drama.'
Writer Eric Saward originally suggested just using it less often, but Nathan-Turner argued that this would just make the Doctor look like an idiot. When he's locked out of the action, and everyone knows he's got a screwdriver in his pocket that can unlock the door, how can he not use it? So, they decided the only thing to do was to destroy it.