As someone who dealt with identity theft, SSN should only be collected if contact with the SSA is needed. I.E. payment of social security benefits.
Any and ALL other "ID", nope. Use some other number.
You wanna tell that to phone carriers, internet service providers, electricity providers, and even water providers?
So unfortunately... they will decline to do business with you if you decline to provide your SSN.
The only logical solution: Government needs to mandate a no SSN requirement and make it illegal to refuse service even if no SSN is provided.
The same goes for credit card and bank account numbers. As anyone you've ever paid with your card or by check has access to these they can't be considered particularly secret. The problem is that the system barely has any authentication built in. 4-digit PINs and hastily handwritten signatures only an expert can verify do not offer reasonable security. Chip cards are a bit better (non-clonable, require physical possession) but only work for in-person transactions.
I always omit SSN, but often can't get away with it.