Ok, this is not a feature request, not in my opinion anyways...
The question is why it isn't there built in facility in phpbb for this (yet), while it is obviously a feature with high demand (Looking back at something like CCP topic, in 2005 if I am not mistaken, f.ex.).
Now I admit I have not really followed the repository actively since phpbb3 went gold, so in that sense I haven't done my homework. However, the sole reason why I am asking this is, because phpbb.com already offers feeds in both RSS and Atom formats the only conclusion I can make is that someone from phpbb team has already written some code to accomplish these tasks, no matter how crude it may be.
With that comes the real question, why could the code for something like this not be "crude" in my opinion for feature such as this there really is no need for fancy stuff like ACP pages or settings (well perhaps two or three settings could be of use, a basic global on/off, feed live time or ttl and max entry limit). Now I know people might disagree here but in truth any other things are redundant.
Because if user can read topics in certain forum it is safe to allow them to access feeds for that forum and via feed url the subscriber could specify the source forum (if subscriber has no permissions return a feed with single entry to inform them of this), feed type and number of items (this respecting the global limit as max and default of course).
In my opinion this is one night job, with the template engine of phpbb (create template for each supported feed format), then again I am someone with way too much free time.
Now I have not looked how any of the existing mods accomplish this, because I am a lazy person, so mods that make changes to core phpbb files are really not my thing (upgrades would become troublesome) so excuse me if I just wrote a page full of useless crap.