Both fair points! In the couple of times I've played it, I haven't had anyone flat out refuse to draw, but I have had people who just didn't take it seriously. I wish I knew of a way to fix that design-wise, but I think that just comes down to who your group is.
I like your "discouraged" idea! For simplicity's sake I don't think I'll include it in the basic rules, but if I find the time to make a major update to the game, I'll add it as an advanced rule.