Well, I mean, mailing a check takes a long time, certainly longer than sending some bitcoin would take, even if it was free. Emailing a scan could work, but wouldn't that be completely trivial to abuse? If someone gets a Gmail password, they could just photoshop a the check to empty out your relative's account with very low effort.

I think blockchain kind of solves these two particular problems; the money transfers are relatively quick (around 20 minutes for bitcoin), and you have all this cryptographic goodness to minimize the potential for fraud.