Unionhawk had a pretty great answer to your question, but let me address a few of your claims that certain things aren't our strengths, because I disagree in many cases:
For finding a specific answer about a specific game, it's certainly
more likely that you can find that answer on a certain site with
game-specific FAQs and message boards.
GameFAQS is pretty cool, and you can indeed often find an answer to your question there. However, often times, you can't. And when you can't, I find I'm a lot more likely to get a quick answer by posting a question here than by posting to their forums. I'm also more likely to get a detailed answer here. Also, sometimes, a FAQ can be so large and cover so much ground that actually finding the answer to your particular question can be tricky, even if the FAQ contains it.
GameFAQs is great, and we certainly have overlap with them, but it doesn't have to be all-or-nothing on either site.
For finding answers about strategy and tactics, you are again likely
to be able to find those in FAQs on another site. Those questions are
frequently not allowed here anyway.
Yes, just like above, you can often find answers elsewhere. Sometimes you can't. Sometimes other places are better. Sometimes they aren't. We don't need to be the single source for gaming information on the Internet. In general, the more popular or in-depth a game is, the more likely you are to find better, in-depth tactics/strategy advice elsewhere. That doesn't mean it doesn't fit here, though, and particularly for smaller games that don't get entire wikis devoted to them, it doesn't mean that this isn't a great place for such questions.
As for them being "frequently not allowed here anyway", that should not be the case. These questions are definitely in scope. They tend to be some of our best questions and answers. I would definitely like to see some citations of general strategy/tactics questions that have been closed. They may have had other problems with them (often, "too vague" or "too broad" are the problem). Or there may be some people who voted to close that I need to go yell at. Either way, I'd love to see them.
When looking for game recommendations, other forum-based sites are a
better match. Those questions are not allowed here anyway.
Yes, this is definitely not the place for those questions. We had them for a while but they just didn't fit the StackExchange format well. Voting on answers tended to be a popularity contest of "Oh, yeah, I remember that game! It was awesome!" People would often end up getting answers, so it was cool that we were helping people, but the questions really didn't help anyone else, make the internet better, or have votes that actually reflected their accuracy. You can read a ton of meta posts about the long arguments we had over whether they should stay or go.
It's not that we don't want to help people with these sorts of questions. It's just that the site isn't a good fit for them. We do want to help! When I remember to, I try to direct people to this Arqade blog post that tells them where they might be able to find an answer.
Community is not a relative advantage - Some members of the community
are openly hostile towards new users if they ask the "wrong" question,
and will close questions even if someone has already taken the time to
answer it. I can think of two examples where this has probably driven
away a new user (unable to verify the older example since I can't find
the question anymore). This does not seem to be a unique concern. See
the related question at What about the new user experience here is
turning people away?
There is no doubt that some of the site policies turn off new users. If a question is off-topic, we close it. If it's bad, we downvote it. This can scare off new users who feel attacked for "doing it wrong". However, we can't simply allow off-topic content just because it's a new user who is asking it, nor should we upvote bad questions/answers just out of pity that it's a new guy asking them. Our goal here is to generate high quality content where the best stuff bubbles to the top via votes, and the bad stuff sinks to the bottom.
We can, however, try to be nice about it when we explain to a newbie why their question was downvoted or closed. Some people are better at this than others. Some users don't even try to be nice. There's not a whole lot we can do about that except, as individuals, trying to personally be helpful to set the best tone possible, and to flag outright rudeness when we see it. There's a huge gray area in between that we can't do much about though. That exists on any gaming site you go to which allows conversation, though.
There isn't much for new users to be able to do. Asking a question may
trigger hostility. Being the second to answer a question may trigger
hostility. They can't comment, and using the answer field to add a
comment will trigger hostility.
I can't really say much about this except "people shouldn't be hostile... sorry if they are" and sometimes factual messages such as "Answers shouldn't be used for comments. I'm flagging this for removal" can come off as very hostile when they're not intended that way, especially to a newbie. Again, some users here are pretty tone deaf. Everyone can be, at times. My comments on your original question could have been better worded, but I was still half-asleep because I hadn't had my caffeine fix yet this morning.
That said, it doesn't take long for a new user to earn enough rep to leave comments. You get that at 50 reputation. That's 5 answer upvotes or 10 question upvotes. It's a network wide policy that many people don't like, but isn't likely to change (probably mainly because otherwise it opens the network up to easy spam). And at 20 rep, they can come to chat and ask questions or leave comments. That's just 2 answer upvotes or 4 question upvotes.