You might think at first this would lead to chaos. I don't think it would. I think it would make the world radically better. I can show this would work if you're curious.
Such a scheme would have the added benefit of encouraging quality products to the point that companies producing poor-quality goods could lose their trademarks to quality companies. So if Dell began producing their own line of "Apple" branded computers, Apple could only sue Dell if the Dell "Apple" computers were causing harm to Apple's reputation. If Dell's computers were actually better that Apple's computers, Apple would have no cause of action. In time, if Dell could show that Apple's computers were actually causing harm to Dell's reputation, Dell could force Apple to pay damages for using the Apple mark.
But a lot of other people wouldn't care, and they'd happily drink the scam Coca-cola which tastes just like the real thing, but is made by somebody else, and is cheaper.