I don’t think that you are going to learn anything as an undergrad at Harvard that you couldn’t learn at a different top 20 or Ivy League university.
If you attend any top 50 university, and if you do exceptionally well, then four+ years from now if you are considering graduate school Harvard will still be an option.
On the other hand, if you want to apply there is no harm in trying one more time. Spending a gap year tutoring inner city students does seem to me like a valuable way to spend a gap year, and is likely to make you an even better student when you do get to university.
I think that reapplying is not likely to result in a different outcome, but you will never know for sure unless you do reapply and see what happens.