The solution to not being "worried that our ID may get stolen" is penalize companies who report false information to credit bureaus and penalize credit bureaus that give out false information. You don't care if someone impersonates you to a lender and a bank or mattress store loses money to a fraudster. You care that the company that lost the money can erroneously report that you defaulted on a loan to the credit bureaus and then the credit bureaus mark down your credit worthiness. This affects your cost on loans, ability to rent an apartment, get a job, etc. The "Fair Credit Act of 1970" gave credit bureaus immunity from liability from reporting false information as long as they don't to it on purpose and in exchange they have to give people access to the reports and fix errors (very hard to do in practice).
People were rightfully worried in recently emerging computer age that these credit agencies would have secret dossiers on everyone. At least this law let people look at them and in theory correct them.
It probably time to revisit that 50 year old act. I'm not sure how much lenders even use the standard scores anymore. Many calculate their own scores and probably include all sorts of info that we would be mad about them using if we knew what it was.