"Protected" prevents newbies from adding silly answers to popular questions. It doesn't stop not-so-newbies, as I just noticed following a link from the flags page.
How about if proposing to answer a protected question, for people > 10 (or > 10 and < N) resulted in a warning saying, "This question has been protected because the moderators think that it's already got all the answers it needs. Do you really have something novel to add?"
Note that a typical user never actually reads the 'protected' banner in this case. They read the question, and the banner has scrolled down. Then they go add their answer. This my suggestion that the act of adding an answer should nag, something like the "you're adding another answer" nag.