Let's see...
Apple Pay Cash can accumulate cash on your behalf, from others. And similarly, Apple Pay Cash can, on your instructions, disburse specified amounts of your accumulated cash to a party you designate.
Smells like a bank to me.
And like a bank, if any transaction is an amount of $10,000 or greater, that transaction must be reported via a Currency Transaction Report along with your SSN to the government. This is to curtail money laundering activities and has been in effect since the 1980s. I suspect there are other reporting laws, likely secret, to curtail other illegal activities.
Again, Apple Pay Cash would not disclose your SSN to a cash recipient you designate. Why would Apple do that? And why would a party you send cash to need your SSN?
If someone sends me money, I want it directly deposited into my checking account. I don't want Apple to hold it like a bank or paypal, so they can get incur interest.