The costs and benefits seem fairly analogous to those of "trolley problems," which is well-travelled ground at this point, so I won't try to cover it again.
If you can see a benefit to trolley problems in general, it seems you ought to be able to see the same benefit here. Conversely, if you don't, then it seems you should have the same objection to trolley problems involving death, torture, murder, and other bad practices.
Personally, I invoke Weber's Law in these sorts of cases: when a posited delta is smaller than the just-noticeable-difference, I stop having faith in anyone's intuitions about it, including my own. Anyone who wants to compel me with an argument in such a case needs to do more than appeal to my intuition.
The 3^^^3 bit makes it qualitatively different from any real-world lose-lose hypothetical. Remember that lose-lose hypotheticals are something that people in power, e.g. politicians, have to decide every day.
Update: Discussion has moved on to a new thread.
After 61 chapters of Harry Potter and the Methods of Rationality and 5 discussion threads with over 500 comments each, HPMOR discussion has graduated from the main page and moved into the Less Wrong discussion section (which seems like a more appropriate location). You can post all of your insights, speculation, and, well, discussion about Eliezer Yudkowsky's Harry Potter fanfic here.
Previous threads are available under the harry_potter tag on the main page (or: one, two, three, four, five); this and future threads will be found under the discussion section tag (since there is a separate tag system for the discussion section). See also the author page for (almost) all things HPMOR, and AdeleneDawner's Author's Notes archive for one thing that the author page is missing.
As a reminder, it's useful to indicate at the start of your comment which chapter you are commenting on. Time passes but your comment stays the same.
Spoiler Warning: this thread is full of spoilers. With few exceptions, spoilers for MOR and canon are fair game to post, without warning or rot13. More specifically: