FWIW, Drew does not start all, or most, answers with ask Emacs. (Nor does he include ask Emacs in all, or most, answers.) Only a tiny percentage of his answers include ask Emacs in one form or another. Only when he thinks it is germane to the particular question - when he thinks it is a question where asking Emacs makes a lot of sense.
The point of not just telling, but showing users how to ask Emacs is to help them learn to help themselves. That's not to dismiss their question or toss them on their own or tell them they shouldn't ask here. Emacs doesn't act that way, and neither does Drew, he hopes.
The point is that Emacs itself is especially good at helping you help yourself, but learning how to ask it is, well, a learning process. And not only for newbies.
But it's not just to help users learn to help themselves, in the usual sense. It's also to point out that Emacs is transparent all the way down (at least in Lisp). This is really the message underneath ask Emacs, beyond getting you to your specific answer. Not RTFM, but Look Ma, you can see inside this thing!
That asking Emacs works, that it is one of the best ways to both learn Emacs and solve problems, is precisely a thing about Emacs itself - one of its most important features - maybe its central feature: You can interact with it. Talk to it. Look deeply into it. Ask it how it works. It's usually easy and often powerful. (This is mostly because Emacs is Lisp. And because it is free software - no hidden implementation.)
This is not something obvious, even today (when apps and languages have built-in doc, contextual help, AI assistants, good search, etc.). What Emacs does to help you - what Emacs is - is not something that most people are used to or expect.
Why not just show them, without adding the mantra "ask Emacs"? Because the message is not just that you can look something up in the manual or use help keys, and how to do so. The broader message is that Emacs is something you can ask Emacs about in other ways too - and they can be worth discovering.
It's not about doc, in the narrow sense. Emacs exposes itself more than just by way of its doc. It's about inspection or introspection. It's about the fact that pretty much every action you take with Emacs invokes a command - typically a Lisp function. It's about Lisp.
You ask, "Is it good way to start an answer with 'Ask Emacs'?" My answer is it can be. Sometimes that's the right help and the right message, beyond getting the immediate question answered.
And it's pretty much always part of the answer, at some level - part of the point about helping with Emacs in general, whether stated that way or not.
You start your question with "Emacs is, as everyone knows, self documented lisp environment with very good Info system built-in." No, everyone does not know that.
How long have you known it, for example? You didn't know it before you knew it, right? You might know all about Info now, and you might be annoyed to hear someone teach it (point it out), especially over and over. You can be annoyed, or you can just skip it and move on to an answer that is a better fit for you.
Can an answer here misjudge where the questioner is at, supposing too little or too much know-how about, or interest in, Emacs? Sure. Maybe it provides just the code for a command that is sought. Or maybe it says something about that code, to help a bit more. It depends on a guess about the asker, and maybe on how interesting the question is (and maybe on how much time the answerer has).
Some people will sometimes appreciate some such extra help. Some won't care. And some will sometimes be annoyed. (And an answer is not just for the person who asked the question.)
Teaching is repetitive, but learners don't usually repeat the same material over and over, and they generally don't get annoyed by things that are new to them. ;-) Here, all levels are mixed. What is old to one is new to another. If you see an answer that teaches you something you already know, consider moving along to one that teaches you something new...