There's another side to it, which you allude to with the give away of credit monitoring services that data breaches result in. The whole reason the data is valuable is for account takeover and identity theft because identity verification uses publicly available information (largely publicly available, or at least discoverable, even without breaches). But no one wants to put in the effort to do appropriate identity verification, and consumers don't want to be bothered to jump through stricter identity verification process hoops and delays---they'll just go to a competitor who isn't as strict.
So we could make the PII less valuable by not using for things that attract fraudsters.
So we could make the PII less valuable by not using for things that attract fraudsters.