Users may only send to users with less reputation than oneself.
So then I could just spambomb the majority of users on SO? I like it!
Pesto, kindly prepare your inbox for unsolicited subscriptions to Laserdonuts weekly and offers to increase the size of your vodka bottles.
Anyway, this is a terrible idea.
My reason for private messaging: Sometimes newbies write horrible questions. In this case it would be nice to give them a private message explaining why they should improve their style. Doing that in a publicly viewable comment (perhaps with others bashing along) is not very constructive...
That's why comments notify the owners of the questions on which the comments are placed. Why do you people continue to insist Team Jeff reimplement features SO already has? How are comments not constructive? Someone who is going to be offended by a comment that says, "Your style could be better" is going to be just as offended by a private message saying the same thing.
Moreover, we have edits so that we can edit things to improve them without even bothering to leave a comment. That and edits have comments themselves so you can provide less-visible edit-related constructive comments there. And new users can learn from example by looking over the changes made by the edit instead of having to figure it out from reading a private message!
EDIT
And another thing. Your suggestion really works under the assumption that users with high rep aren't assholes. I have an example of a high-rep asshole right here. Seriously. If you give me a feature that I can abuse that I think needs to be improved I will abuse it until Jeff fixes it in a way that satisfies me, or gives me a logical reason why I can't have what I want. Any moderator who has been reading my spam reports will back me up on that one.
Don't take this as a threat - take it as a prediction: I will spam you and everyone else who suggested the addition of private messages on SO if they get implemented. Ask any moderator about how creative I can get and how serious I am.
Now as if that isn't enough I'm going to eat this knife to back up my claims.
EDIT2
It boggles my mind that even after my stunning display of knife-based imagery this question's vote count is still greater than zero. How many more logical holes must I find in your silly idea before you social networkers understand the point of SO?
You want to send messages to new users because their questions suck. So fix their questions and leave a comment in the edit history so they know why you made the change, and they can see the specifics of the change you made so they can make it themselves next time.
<strawman>
But wait, that's too aggressive! These poor new users' feelings will be injured and they won't grow up right!</strawman>
The way I see, someone humble enough to ask a question on an Internet Q&A application shouldn't have a problem with people making his question better, and offering him help publicly. Oh no! He's gotten help! The poor bastard is going to have to cry himself to sleep tonight on his bed of empty beer bottles and broken dreams.
(Broken dreams are very comfortable, by the way. The more hopeful the dream the fluffier. Like kids who want their favourite baseball man to sink a 4-point dunk past the 90-yard line when the score is already 40-luv. Those are the best!)
You seem to think that a private messages' usefulness is an obvious truth. It's not. You have to demonstrate to me that you are capable of predicting human behaviour as The Atwood Superfriends have in coming up with badges and reputation to curb actions toward the main goal of the site. You have to prove that your system works in practice.
You haven't done that. You've just said, "Hey, this is good." That's not good enough. You should know that.
EDIT3
It's an injustice that you're not listening to me. You're probably off closing my answer like you closed Click Upvote's. I can see you mods there, with your devious plans and your fancy ornithopters you use to commute to moderatorville every afternoon.
I'm entitled to having an audience who supports my ideas! That's why I can just keep posting the same suggestion over and over again even though you've shot it down (n-1)
times before!
This is good knife. The taste is a bit dull, though.
EDIT4
You've even killed Shog9, my Internet acquaintance! Haven't you done enough!? What more do you sick private-messagers want? Whom do you have to kill next before your bloodlust is satisfied?
Your cause can't be forwarded this way, you know. Violence begets nothing but more violence. I think Napoleon said that. Or was is that guy from Star Trek? It doesn't matter who said it! The point is killing Shog9 proves nothing other than you're an inhuman monster. People don't like inhuman monsters. They downvote inhuman monsters. That's all you've accomplished by killing him. Downvotes for your entire cause.
If I put up your cause on the Internet, absolutely no one would Digg it. You wouldn't find it on Fark (except with possibly the FAIL tag). If it showed up on Youtube in a video format its rating would be one star out of five. Or maybe Google would change Youtube's rating structure just so that your cause's video-ification can have the implausible rating of zero stars out of five. Wouldn't that be fantastic?
We live in a brave, new, Shog9less world, people. A world where things can have no stars. Look what you've done.
EDIT5
When you get your way and the world is destroyed, it'll be just you and Stack Overflow and the wide open world. Forever. The world where all the people who hate you are dead.