This sounds like a very good activity to me also.
You have requested that we do not say “do what you love”. I would instead say “do what is right for you, and do it well”. This may sound like almost the same thing, but it is not quite the same thing. You might love eating chocolates and sitting and watching TV. That does not necessarily mean that eating chocolates and watching TV are the right things for you. Doing something constructive and worthwhile will take more effort, but is likely to make a person happier in the end.
Teaching kids science sounds very worthwhile to me.
In terms of your “Cons”, prestige does not matter. Doing something constructive and worthwhile does matter. Helping other people matters. Anything that you do will leave less time for other activities. To me this looks like something that will take enough effort (for both you and your students) that doing it for more than a month might be tough, or might eventually drag on a bit. One month is plenty and is enough time to make a difference. On the other hand, your “Pros” all look valid to me.
And you might want to read the “applying sideways” blog on the MIT admissions web site. A quick Google search should find it. The same approach of “do what is right for you and do it well” has worked for us at other “top 50” universities and not just MIT.
And whether you want to do this is really your call. If you decide that you want to do it, then to me it looks like a very good activity for a month in the summer.