David killed Goliath with a sling, not a slingshot, which is an entirely different animal.
Having come under fire from some Arabs with them on the Lebanese border of Israel, they're no joke. Anyone without a helmet (like I was) and half the guys WITH helmets could have been killed if those idiots had any accuracy. They were hurling cobblestone size rocks at 50-100m. The IDF was shooting back with rubber bullets. That was nice, because the Arabs were going for the lethal option, and I'd have just shot them.
David was using the smaller golfball sized rocks going by the descriptions, with serious accuracy and lethality. The Roman army used slingers with lead or fired-clay "bullets" for the same reason. Against a massed target (think rioting mob) what's basically a patch of leather and two strings can effectively deter or injure people at short rifle distances...accurately, with practice. Even lethal option if it came down to it. I don't think we're going to have a new magazine called Slings & Spears Weekly, but remember it's not weapons that are dangerous, it's people and their minds.
Technology and training go hand in hand. If semiautos got banned, we'd be using 100 year old technology with current optics and options and training. A good man with a bolt action can seriously raise hell. It wouldn't be as easy or as 'cool' as a modern AR, but a rifleman with a bolt or levergun teamed with a second person with a shotgun has pretty much all the bases covered.
Same thing armies did in the 40s and 50s, having 2-3 guys with SMGs and a squad of guys with bolt guns are semiautos to cover close and long range.
Ruger wouldn't be the only one building Scout-ish rifles in that instance, and there'd be a resurgence of popularity in leverguns, whether traditional tube feds or the '95 Winchester/Savage 99/BLR mag fed types.
A .308, 7mm-08, .270, any of the medium 7mm sized rounds, topped with aperature sights and an Aimpoint or fixed 2X would be the apex of WW1-WW2 technology level fighting rifles w/o going to a semiauto action. It'd be back to slightly heavier calibers and trying to ensure a first round hit was a channel changer, rather than multiple smaller caliber hits, fast in the same place.
Your average .30-30 or .357 levergun will still defend a house quite well, especially with modern updates (XS sights, a weaponlight) if it comes down to it.