The practice you describe is actually quite common in the slightly different form of a research statement. See my comment above.
Would it be an acceptable practice?
This seems to be a common question around Academia.SE and comes up in many different contexts. My opinion on such things is that this is usually not a helpful question to ask. For a practice that is not common (say, reciting Shakespeare in a calculus class), there will likely always be at least one person who finds it objectionable or "unacceptable". So rather than worry if it is unacceptable, I suggest focusing on the separate question of whether it is a good idea. If it is, go ahead and do it. If it's not, don't do it, regardless of whether it would be acceptable or not.
Would it be an advisable practice?
Well, as you yourself say, it could turn out to be awfully time-consuming. However, I can definitely think of situations when it would be advisable. If your result was applied in a key way in Prof. Humperdink's recent proof of the famous Griemann Hypothesis, absolutely find a way to tell the world about that. More seriously, as you create a body of work and your work is applied by others in various ways, there can definitely be a lot of value in creating a short summary that allows people interested in you and your work (e.g. colleagues and prospective and current employers) to get a quick overview of your work and its importance. The precise title of the document ("Research statement", "Research summary", etc.) and how is it formatted (PDF vs HTML, etc.) are not so important as long as it's presented clearly and easy to access. Similarly, whether the document summarizes your own papers or whether it summarizes the use others have made of your results (the former practice being more common than the latter, as you observe) does not make a huge difference in my opinion; you can have two separate documents to discuss those two things, or cover both of them with a single document, which could make a lot sense since in many cases they would logically fit together very well. Or you could just cover one of those two aspects if that makes the most sense to you.
The important thing is that any survey that you prepare of your own work be written in good taste and not in an excessively pompous or self-aggrandizing way. If you make wildly exaggerated claims about why your result is revolutionary, groundbreaking, deserves to win some major award, etc., this will leave people with a bad taste and they will quickly develop a discounting factor that they will apply to any future statement they hear from you. (As an example, a friend I had in grad school used to make wildly exaggerated claims in a humorous fashion, leading to some of his other friends inventing the "log" rule, which was that you had to take the logarithm of anything he says...)
Should only the works that build directly upon the cited paper be
included in the list (or should one be more flexible and include also
papers that are less strictly related)?
It's hard to say. My inclination is to say that you should generally focus on the papers that build more or less directly on your work. In certain cases, say if a paper you wrote was used by someone to invent a whole new theory, which now generates hundreds of new papers every year, it may be reasonable to say that your paper played a key role in the creation of the theory and led to the later wave of publications, even though its contribution was of an indirect kind. Again, the key rule of thumb is that your claims should be seen as reasonable and presented in good taste, with the goal of genuinely helping the reader to understand the development of the subjects you have worked on, rather than to make yourself seem important by claiming credit for anything under the sun that your work has touched on in any way.