I've tried various sling and shoulder bags for bike rides and hated 'em all. Mostly because of old neck and shoulder injuries -- I hate any weight on my neck. But on a small group ride Friday evening at least six friends carried various sling bags and seemed to have no complaints -- those types with one strap over one shoulder, the other strap around the waist.
The one bag I'd consider is my knockoff
2-liter hydration backpack, which I've mostly worn for 3-10 mile jogging/walking sessions this summer. It's low profile, not too heavy even with a full hydration bladder, sits well on my shoulders and back without shifting or flapping around, and has good organizer pockets. I'd even consider using the main pouch for carrying other items if I didn't need the hydration bladder. Or with a half-full bladder, I could stuff a few other items such as a packable windbreaker/rain jacket in the same compartment as the bladder.
But I'd rather let the bike carry stuff and keep it off my back. I don't mind overstuffed jersey pockets and occasionally carry a second or third tube, CO2 cartridge, a few tools, etc., in the middle jersey pocket.
However I can see why some folks dislike handlebar bags. They can affect handling and tend to make the bike feel heavier, even when it's the same or less weight compared with a backpack or rear rack bag. I've used handlebar bags, but I can't say I've ever liked them.