Recently there have been a number of suggestions for a separate 'newbie' area to deal with the perceived distaste of answering simple questions. I don't think that people are tired of answering simple questions, but, as you say, are tired of poorly-formatted questions that make it clear the person didn't consider RTFM (granted, the person may not know the manual exists, but the basic search facility on the site is obvious enough). Having a separate area for these types of questions might be better than a complete ban of impromptu questions and could address the source of frustration.

What I suggest (without completely backing it myself) is a distinction between anon and non-anon posts. The proposed waiting period as well as other possible measures (for example, displaying a random site tutorial instead of the gates at first connection) could be applied only to named accounts. Deciding to register a name would then demonstrate an intention to participate in the site. Anon postings could be free of such restrictions, which means that someone could still pop in, ask a question, get an answer and never return (but perhaps go on to build some amazing free software tool, for all that we know).

Once the questions are divided (roughly) into member and non-member questions, an option could be added to 'display (or not) anon root-level posts'. People who want to could concentrate on the (possibly) researched questions, and those who don't mind the other questions can go right on answering them. Since there's already an option to not display unapproved posts, I don't think this would divide the monastery too much (but I may well be wrong).