I think we should adopt the process MSE's index uses. That formalises our current process, basically, in which anyone can ask a question, and a combination of community activity and mods judging the proposed FAQ to be mature results in it being tagged with the mod-only faq tag. It would just be a clearer and cleaner set of instructions for that.
I'd propose adding this text to the end of our FAQ index:
How can a question be added to this FAQ?
Ask only the question, stated plainly and simply, in the question body.
The answer goes in an answer.
Link back to this index. Paste this at the end of the question:
[Return to FAQ index](/q/7064)
Tag as faq-proposal and support. When a post seems
to have hit a mature state, it will have faq added by a moderator.
Flag for a moderator to mark community wiki. Any FAQ post not yet
community wiki should be made into a community wiki.
After the post has the faq tag added to it, add a link in the above table of contents.
(This has minor modifications from the original, just making the tag names and index links match our site.)
A minor con
The one con for this is that, over time, we'd want to rework our existing FAQs to follow the instructions to make the meta Q be just a plainly-stated question and leave the answering for the answer posts. Our current FAQs are all over the place in terms of their structure.
Reworking them is something that I think would be a somewhat low priority though, and wouldn't meaningfully impair the value of the set of FAQs as a whole (after all, they work now), or impede using this process for future potential FAQs. It's something we could work on over time.