I think that you have to distinguish between wars in which the outcome is uncertain—that is, wars in which real risk to both sides is present—and wars that are essentially a big guy beating up a little guy.

I agree that the former kind of war would happen with the same frequency if this pen pal idea were implemented—the motivation for such wars need to be large enough to overcome the personal danger that they produce, and so would easily overshadow semipersonal connections with citizens of the opposite side. I think that the latter would very much be deterred, though, because the motivation for such wars can be miniscule, to the point where even the humanization of the "enemy" could be a significant deterrent.