Those checks you talk about, involve using SSNs at some point. Also, these checks are not scalable.
I think, because you have not lived within a system without an id mechanism, you have no idea of the set of challenges you face as a business as well as an individual. Just think how would you prove to a lender your financial status. You would have to give him a copy of documents of all your assets (bank statements, property documents), copies of your tax returns.
Because as the previous commenter mentioned, you’re then in the position of needing to share out much more intrusive info to many more people. It’s also a pain in the ass from a customers standpoint given the statistical rarity of someone being impacted by ID theft.
Sure, a photo copy of your ID and your address might seem more personal but ultimately the SSN is just as personal because someone can ruin your life with that one number + your name. In that sense it seems like you are already giving out the most personal of information to some random employee at said business.
Those examples are for getting a phone or electricity connection. For a loan, you would have to give bank statements, income tax return proofs etc. And if that is not sufficient, you need to get your property apprised by "authorized" valuators!
How does schools do background checks? How does the police force do it for their officers? Why can't the same method be used for a bank?