Interesting idea and I take your message to heart that we must not ignore the possibilities and advantages of the sling. Hell, I'd support it just on the basis of honest recreation. On the other hand, as far as self-defense is concerned... a sling seems to have a fairly limited application. More or less, to kill something at a distance that you know is coming.
As an avid knife thrower, let me suggest something (no not throwing knives)- or rather agree with something you started saying- everyone learn to throw with accuracy and power! It's FUN! You need this skill for several sports anyways and opens up recreational activities like baseball, boomerang, darts, knife/spear/hatchet throwing, etc. It's healthy. Get outside more, good for warming up (pacing from the target back and forth, bending to pick up thrown objects, etc.), builds co-ordination and strength, etc. Finally, it's good for self-defense.
Floyd Lee Fugatt (master knife thrower) says: A 4 1/2lb singlejack [hammer] will stop a 2000lb bull dead in the grass. I know cuz I watched my Grandpa do it. The hammer has several advantages over a bladed weapon. 1.) It don't get stuck in bodies. 2) Blunt trauma has way more stopping power than bleeding the critter out. 3) They are common and not difficult to find. 4) They are legal to have and have other uses so the questiion "Hey boy wachu doin with dat hamma" has easily believable answers. The Viking types often attached a long rawhide thong to a short handled hammer so they could knock the crap out of horsemen and snap the hammer back to their hand. I have done this and a quick WARNING is that you don't completely miss your target. You are likely to have your arm yanked real bad otherwise! A 3lb ball peen hammer is also easier to conceal and carry than a gun cuz there ain't no sights or triggers to worry about.
My own submission is if we simply carry around smooth stones (flat ovals that fit in the palm), they'll work as a fist-load for straight punching, hammer w/ a downstrike, and a deadly projectile. It can sit in your pocket as a "paperweight", keepsake, or- under questioning- simply a rock you picked off the street. So you've got a concealed and legal weapon that's quickly drawn and used both in CQ and at range.