First, I don't think the only or necessary consequence of people owning their data is that no one else can use it or make something of value out of it.
Think of it as a raw material that individuals own as they can mineral rights. I can imagine circumstances in which individuals may want to sell (or lease) their data to companies that might sort, aggregate, analyze, qualify or otherwise manipulate it to create some salable information. Just because companies get it "for nothing" now, doesn't mean it has to be that way for companies to make a profit.
Second, if companies want to charge for products or services that are now "free", fine. Let them. Then consumers can decide what such goods and services are really worth to them. They might discover that a lot of them are only worth the price when the price is zero.
Always look over your shoulder because everyone is watching and plotting against you.