Paypal is the most convenient way to pay for purchase both in the US and overseas (as they convert the funds to foreign currency for you).
But if they think someone can put a social security number online and have it be safe, they’re sadly mistaken.
Requiring that will just be the end of Paypal—a useful service; and instead we will go back to sending checks by snail mail, waiting for them to arrive and clear, and then getting our purchases.
This won’t accomplish anything but the death of a useful service.
Actually it will just make merchants purchase a credit card machine. You will call the merchant to make the purchase and give them your CC# over the phone to be keyed in.