It isn't that
nobody cares. Many people definitely care. Maybe not everybody cares, and maybe even among those that do there's only some subset that's actually capable of proposing effective solutions to the problem. But I know plenty of normal everyday people outside the techsphere who would prefer if data privacy and authentication worked better and are scared by data breaches like this.
The apathy is really more of a practical matter -- they don't feel like they understand the problem or know how to solve it, and they don't feel like they'd have the power to do something even if they did.
They correctly realize that we don't have a system where entities like Equifax are accountable to individuals that care. The only way you'd get that accountability is through some kind of collective action.
Same thing is true for widespread adopting of PKI-based schemes. Saying "nobody cares" is about as true as saying nobody cares if the oil in their car gets changed -- they don't want to have to pay attention, they don't want to invest in understanding/adopting, and maybe rightly so because there's so damn much that already requires attention. But you might get adoption among private institutions that matter by some kind of legal policy.
A state-run identity registry and authentication solution isn't the only way, to be sure, and I think it's a weird shibboleth in the context of democratic republic run by elected representatives, but since it's not the only solution, nobody needs to die on that hill.
But by the time you're talking about society-wide improvements that address the relevant problems, you're almost certainly going to be invoking government-like powers. The issue you've discovered here isn't about who/how many people care, it's about one of the limits of market-like institutions to transform some forms of concern into effective action. Something even for people who don't trust the state to think about.*
(Also: "people who use this kind of language to insist that the only way to achieve this is through the state are just looking for excuses to be mean to people who don't trust the state" deserves an eye roll so hard. It's manifestly true that there are people out there who enjoy trolling, but the idea that's the only possible motivation is a non-starter and not a good way to indicate you yourself are approaching a conversation in good faith.)
(* I also don't trust the state, just like I don't trust many forms of private power. But it turns out both can be situationally useful and beneficial if you can get the balance right.)