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!