So you raise two seperate issues here, which I'll try to address in turn.

First, as regards the FAQ. While it would be great if every single question asked here could get an amazing, tailored answer written specifically for the OP.... that just isn't going to happen. A lot of questions don't get noticed at all, or they do, but don't get the answer they deserve. And while we have nothing against repeat questions, it can get tiresome answering the same thing multiple times, so you'll see very common questions will often just get ignored. As such, we maintain the FAQ, so that if someone asks a question which is similar to a previous one, they aren't going to be left totally high and dry. As you note, there is... variety... in how people are directed to the FAQ.

To start though, the thread you link to is something of a special circumstance. The OP (HI!) is also the author of the linked answer, so while them providing a quick TLDR of their own comment is totally kosher, when someone is linking to another users comment, while including some brief commentary of your own is fine, we prefer that the user doesn't go overboard in summarizing the linked answer. What is the line? Ask Potter Stewart. Generally speaking, we have a decided preference in how FAQ linking be done. Super-kudos go to the users who write something along the lines of:

Hi there! This is an interesting question, and hopefully someone will come along who knows the answer, but in the mean time, you might be interested in the response written by /u/Thisisafakeusername in this answer, which is somewhat similar to your own. It addresses [one sentence summary of the piece].

It hits everything we like to see. It is friendly, doesn't in any way try to discourage repeat questions, and provides a specific answer. Bonus points for using a username ping of the author to let them know that people might be reading their own post. Especially in the case of archived threads, it means they can show up to answer follow ups hopefully.

Now, if there is a right way, presumably there is a wrong way. In some cases, there are things we prefer not to see, but let slide. People who link to an old answer, or to the FAQ section, without any additional commentary, for instance. In the end, something like that is essentially neutral. But we do generally remove comments which are unnecessarily rude or not actually helpful.

• People who say something about using the search feature.. - reddit's search function actually kind of sucks....
• People are are dismissive about the question being a repeat. - Few questions can ever be TRULY answered completely. There is almost always more that can be said, or a new angle to be gained. Us mods are the ones who see more repeats than anyone else, and we don't mind it, so you shouldn't either!
• Links to shit threads. - Often people search for an old thread and link it without actually checking it. We check those links though. It is amazing how many times people link to thread where there isn't actually an answer.

That is just a few examples.

So anyways, the point is, linking to the FAQ or old answers is a useful service, and we encourage people to do it, but we ask that people be polite and helpful in how they go about it.

Now, as to your second issue, with the "responses along the lines of, 'This is a very broad question.'" As is well known, we do try to get questions to be specific here with our so called "Trivia Seeking Rule", but we try to balance that with nevertheless allowing wide interpretation of what being specific means... I'll quote from a response I wrote to someone who was complaining about the opposite end, namely that we are too broad in our allowance of questions asking about "Medieval Times":

I sympathize, since I know it can be frustrating, but I also sympathize with the OPs in these situations. Most people asking questions here are laymen who don't know much about the period. While some of us here could no doubt break the Middle Ages up into a multitude of sub-periods, each of which would warrant its own, different answer to some of the questions that get asked, to them, it is just "Medieval Europe", or "The Ancient World" and "Pre-Columbian America" which frankly I think have it even worse. Insisting that OPs specify that they mean 13th Century Aquitaine or 10th Century Wessex maybe will make it easier to answer the question, but also will just dissuade people from asking them in the first place.

Now, I'm not saying we should just ignore the uniform treatment of these vast, often millennium spanning periods by the questioners here, but on the whole, I don't see much value in simply interrogating them to narrow down a "when" and "where". Even if they give you a specific answer, I'm doubtful that it is one that really feel passionate about. They probably don't care a lick whether you are speaking of 12th century England or 14th century France, or 9th century Italy. Those people, I'm sure, don't even understand just how different the answers would be depending which they ask, and as I see it, the approach isn't to say "Can you narrow that down?" but use your answer to help them understand the diversity of the period.

So while I get that you feel lack of specificity can be a turn off for people who might answer the question, the flipside is also true, as I think that insisting on specificity will turn off many people who are wanting to ask questions. Asking a good question is no easy task, and I don't think it is a stretch to say that there is more chaff than wheat here no matter what the topic is. AH is, or at least strives to be, an intersection between academics and laymen, and frankly, for better or for worse, we do need to be understanding of the latter's limitations, one of the most glaring of course being that they don't always know enough to narrow down their time period beyond 'the big ones'.

Which is all to say... yeah, we don't always like to see the responses about how a question is "too broad". I mean, sometimes it really is, to be fair, but simply saying "This is too broad, narrow it down" isn't helpful. We much prefer to see responses which point out how broad the question is, but try to be instructive, and spend at least a little time explaining why this is the case, and offering some pointers on how to narrow it down. So as long as a question doesn't violate the guidelines we, as mods, use, we often will remove the "This is too broad, narrow it down!" comments which we deem to be non-constructive or otherwise unhelpful.