Assuming you live in the USA.

Short answer:: No.

Long answer:: yes but you’re basically living as a criminal, rather— you’d have no bank accounts; no credit cards; and you’d live on cash alone paying no taxes as you’d have to work under the table ( no one messes with the IRS). — or— leave the USA and do the above…

So if you want any kind of “modern life “ put a freeze on all your credit accounts and check them annually

It's not just a breach you have to worry about. Credit agencies actively monetize your financial data by selling it to anyone who wants it. You didn't give it to them, you didn't authorize it, they collect it and they sell it.

https://www.equifax.com/business/marketing/

It's quite easy to get rid of all that crap: just come living in the EU

In a general sense, you are discussing a way to control other people and organizations, and to make them stop talking about you. (Communicating and storing your information) This isn’t always possible or practical.

If you pay a merchant with your payment card, that merchant is allowed to know your payment card number. If you call a toll free number, the recipient of your call is allowed to know your phone number.

If they decide to share what they learn about you, and they do so legally, there’s not a whole lot you can do to stop them. I’m not saying this to antagonize or hurt you. I invite you to think differently about what you can control and what is worth worrying about.

I never asked for a credit score.

Unfortunately the credit agencies don’t have much reason to care what you want. There are people with money who asked for everybody to have a credit score

This is the result of having too many "nothing to hide" idiots.

They are all meaning to say "not my problem", but all they're doing is create problems for themselves and their kids. They only notice, as always with privacy, when it's entirely too late.

I don't think you can. A credit score and a credit report is what companies use to determine if you can get credit from them and at what terms.

If you are in the USA, freeze your credit. So many data breaches happen to millions of people regularly. Be safe.

perhaps if you open a company, pay with corporate accounts - but this is more obfuscation than a solution

Where do you live?

The best you can do is freeze them, you just have to do each on separate on their respective websites.

If you have a SSN, you have a number.

Well I totally get this entire system is mismanaged horribly designed from the start not even designed for this from the start, exetera....

Having some kind of standardized way of stating someone else's trustworthiness when it comes to money lending it's something that's just inherit to capitalism as long as you have capitalism simple as that, even if they don't call it a credit score.