Ol' Pops is on the right track - the original intention of the Protected status was to block non-answer answers from drive-by users:
We needed this because some of the more popular Super User questions attracted a lot of noise from random drive-by users who didn’t understand how our system works — users who helpfully provided so-called answers like “thanks, this worked for me!” or “I have this problem too, can anyone help?”
At one time, the "association bonus" made this a non-issue for folks who were already familiar enough with the system to garner 200 points on at least one site. But last year, the check was changed to ignore that bonus - you must have earned at least 10 points on the site where you wish to answer in order to post an answer to a protected question.
This actually makes some sense: even though Protect was originally intended simply to prevent the worst of the non-answers from getting posted, in practice it's often used on questions that have simply garnered a lot of answers - the implicit message being, it probably doesn't need another one. It's still considerably less drastic than locking the question.
Yes, it has the unfortunate side-effect of blocking answers on those rare occasions where someone with plenty of experience on one site jumps onto another one with a great answer to an already-popular question - but this is always the down-side of Protect; I got an email just yesterday from someone new to our network who wanted to post an answer to a Protected question, with every indication that he was an experienced expert in the subject matter and did not plan on posting a non-answer. Blocking him served no more of a purpose than blocking you would.
The real solution here is to avoid over-using Protect. Certain individuals seem to think it's needed preemptively on controversial questions, closed questions, etc... If you see it being applied to a question where it serves no purpose - or if you simply have a great answer you can't post because of it - flag for moderator attention and ask them to review.
Otherwise... Post an answer somewhere else, and one up-vote will remove the restriction. Frankly, if you can't do that, it's hard to make the argument that you should be posting on a Protected question anyway.