The property you’re talking about is orthogonal to questions about who has the right to control what information.
I fail to see a problem here. "But that's not how it works today," isn't a problem imo.
Let's say we made recipes broadly patentable. I'm sure that would change the restaurant industry into something unrecognizable over time. 100 years from now we'd see all sorts of massive businesses profiting in ways that are unimaginable today. Those businesses' existence wouldn't imply the laws were good. However I'm sure somebody might say, "But how is MegaPizzaWorld ever going to justify its $10 billion investment into monopolizing pizza if anybody can just copy it?"
Then certain restrictions are enforced on processors and controllers with data subjects having certain rights recognized.
The rights and restrictions differ from ownership semantics sufficiently that it's not useful to talk about as owning.
But if you ask the average layperson or watch popular media about data, they speak and think in terms of ownership. That's the wrong model, and it leads to the wrong assumptions and conclusions.
From what I understand, this wasn't always the case. The belief rose alongside the term "intellectual property" in recent decades, which was itself popularized by media companies who have the rights to lots of information, and who stand to gain financially the more we shift toward conceiving of these rights as permanent ownership.
Information is non-rivalrous. It cannot be "stolen" in the same way that, say, an apple can. If I take your apple, you no longer have it. If someone repeats your information, you haven't been deprived of it. These athletes are as free as ever to collect and share statistics about their performances, regardless of who else is also doing it.
When you move through the world, you emit information, but that doesn't mean you "own" it.