Replace it with rights related to allowed uses of data to be determined by the people who produce the data

That's essentially what copyright is! It has more to do with who has the legal right to access, modify, and distribute content than it does about copying. You can make as many copies as you want of content you legally have access to, you just can't share it with anyone you aren't permitted to share it with.

I think copyright is a good thing in general because it gives producers of content some rights to protect the content they've created, which means they have an opportunity to profit from it before competitors can take that content and redistribute it themselves. if there was no copyright protections, the moment you publish something, a competitor will rush to reproduce it and publish it far more broadly, using their much larger distribution network to cut you out of sales.

The problem is that it also restricts modifications, so if someone produces something, you need to be very careful to stay within the constraints of fair use or you could get hit with a lawsuit, and you can be sued even if you've done everything properly if the original creator has enough money to tie you up in courts (see Palworld v Nintendo).

people the data is about

This seems incredibly problematic because then you'd have to jump through massive hoops to write a book involving any public figure. Even if you exempt public figures from this, you could still have tons of lawsuits from people trying to take a cut from your profits if anything in the book seems to relate to them.

The main problem, IMO, with copyright is how long it's in effect for. The original intent was to protect content so the creator could have time to profit from it, but Disney has lobbied in the US to extend that to 95 years from date of publish, or 70 years after the death of the original creator, which is unnecessarily long. Copyright used to only be 14 years, with an optional 14 year extension (subject to approval), and I think that's much closer to reasonable than the current durations. I'd even go so far as to say it should be more like 5-10 years, with an optional extension that's only granted if the creator can prove they need more time to recuperate costs (perhaps a max of 20 years?).