From the Help Section:
What are protected questions?
A protected question prevents answers being added by anonymous and very new users.
Questions should be protected when they are garnering lots of views and newbies are adding "me too!", "thanks!" and possibly even spam non-answers.
Which questions can be protected?
Any question at least a day old can be protected and unprotected by users that have the privilege, provided the question has received at least one answer from a user with less than 10 reputation (such users would then be prevented from posting further answers after the question is protected).
In that section there's a link to the article New Protected Question Status from which I quote:
if you see a question that is attracting a lot of drive-by noise answers, please flag it for moderator attention. We’ll turn on protection. The protection bar is extraordinarily low right now — you only need >= 10 reputation to post an answer to a protected question — but we think this is enough to cut down dramatically on answer noise for certain unlucky, but obviously popular, questions.
So, the purpose of this feature is to reduce this "answer noise" when, for whichever reason, a question becomes popular and starts getting this kind of unwanted contributions from users that are not familiar with the stack mechanism.
Your scenario is significantly different, since you want to discuss protecting a question that has not yet attracted a lot of "noise" answers (or doing something that only a mod could do).
If you can see or foresee a problem with a question you can:
Comment about that in the question post. Comments are used to ask clarification or to add more info, but they can also be used to point out problems in the post or to add some advice or guidance (for example, to help the OP to make their question on-topic).
You can post in Meta, so the community gets aware of the (potential) problem and discusses and addresses it if needed.
You can flag for moderator attention. The fact that you have the mechanism available doesn't mean that every request is necessarily and automatically a good use of the flag functionality even if the indicated problem was to be addressed.
You raise flags to make moderators aware of content that requires their attention. I encourage you to familiarize yourself more with the flags mechanism. In the flag you need to explain why a mod needs to intervene instead of following the many other regular courses of action available (for you and the mod). The mod may see your flag as valid or decline it if the flag was inappropriate - per flag/request basis.
Basically a flag says "I need someone to use their superuser privileges to go out of the regular workflow and do this for XYZ reason(s)". A moderator may think that there is merit in the flag, but not necessarily that the situation needs to be addressed, or addressed in the way you suggest.
For example, if you asked a mod to close a question (even one that is blatantly off topic) the mod may decline the flag and ask you to cast a vote to close (even if they later go and single handedly they close the question themselves, because that's is how you are supposed to proceed in that case).
Similarly, if you asked a mod to protect a question, they may decline the flag if you have enough rep to do it yourself.
If you asked a mod to protect a question because it had a couple of "noise" answers, they may mark the flag as helpful if they see you have a point but not necessarily protect the question (it's OK that you brought that to their attention, but they may decide that it's not the time yet to protect the question). Another mod may have resolved in a different way. After all, the decision to when it's necessary to protect a question is rather subjective.
If you were asking for preventive protection, you would need to convince the moderator that the question needs to be protected even when it has not yet received the very first "noise" answer. Likely, but not necessarily, the mod may decline the flag and direct you to other courses of action.
To summarize, the fact that the mods think that a flag is valid and that the situation it describes needs moderator attention are actually two separate things. Also, many other factors are considered when mods review flags (for example, is the user still in "learning mode" with these features? What's the intention behind the flag? etc.)
"A protected question prevents answers by anonymous and very new users. Questions should be protected when they are garnering lots of views and newbies are adding "me too!", "thanks!" and possibly even spam non-answers."
. What kind of scenario are you envisioning for a question to limit/filter the users that can answer it as soon as it's created? What does "getting out of hand" mean in this context? Why the need for "quick protection" (vs. the standard procedure of waiting one day and waiting for the first answer from a <10 rep user)?